Tuck pointing is in my books re-grouting between bricks, stone, and may include putting grout in cracks to seal up any of those. Is this what you mean?
Grout will dry to the touch in an hour's time. If was was me I would tool the grout in, smooth it off (using a tool which indents the grout so it is recessed from the brick, beveled nicely) then go back in 30 minutes to an hours time to lightly brush any excess off. Large clumps I pick up immediately, I tend to take a bucket for the dropped "dirty" material just to keep a tidy work site. In cases where the wall is old, I attempt to "knock off" more grout to match the older material. I finish off with a bit of a rinse to get a clean surface - unless it is a small job and the grout is fresh.
Grout usually is a mixture which needs a little pressure to seal it into a crack or onto a surface, meaning clumps may fall and stick to the surface but a stiff brush will knock it off easily. The act of pressing it into a crack will cause the contact to be complete, thus when grout dries it is difficult to remove.
If they haven't returned in a month's time they think they are done. If you already paid them this is like "signing off" saying that you find the work to be completed. If you have a contractor managing various projects who also been paying from a budgeted amount, then it is time to get on the contractor about this.
Did you specify before the job was started you wanted it cleaned afterward? In all seriousness today's craftsmen tend to have sloppy work habits and need every little thing pointed out to them, written down and will not take an extra step if it isn't on paper. If it wasn't on paper then you may have to clean up yourself. Sorry.
If you don't have a contract that says "clean work" specifically. Then you will need a stiff brush (Steel) a stone chisel I call them Cold chisels since I came from a part of the country that applied strange names to things -

(Which is a solid steel chisel with a semi-sharp tip. Not to be confused with a wood chisel which has a finely sharpened tip and usually a handle with a grip) and a decent hammer (any will work)
Most of the debris will knock off easily with a brush, there may be a few lumps of material which require a gentle tap or two. Place the tip of the chisel against one edge where the material meets the brick, then lower it to where the flat surface is nearly flush with the brick. Tap gently (If it seems like I am treating you like a child I'm not) If it doesn't come off with one tap, approach from another angle. Meaning if you placed the chisel against the top of the lump, move to the left or right and gently tap again. Gentle Taps are all you should need.
The angle is important, it will direct the energy at a plane with the surface of the brick. If you tap gently working around the lump, you will "break" it off smoothly. Each tap will loosen the material a little. This will knock off the whole piece in one lump, instead of getting an uneven break leaving behind an un-grabable thin slice of material (Thus my seeming to treat you like a child there) You may still have a little bit of material left, a brush will most likely finish it. Gentle Taps are key here, they will "crack" the crystalline structure of the grout in a series of directed blows. You may hit it once hard, but you have a far less chance of getting the whole thing in one blow and find yourself facing a raised patch of grout which is nigh unto impossible to remove.
Second part, an unasked for part, but I think this will help you in your home improvement process:
If you are planning on doing anything else and hiring a worker/contractor to do the work, please fly it past us first. I think we may help to give you some idea of what you need to know about the subject and what to ask for specifically IN THE CONTRACT to get what you want for specific jobs.
I recall you had a couple of other things that were not done up to snuff.
You may have to "stand" over the worker. No, not standing there through the whole job, but come out and see what is being done, how he is doing it and if he isn't doing what you want as he does it you can mention that you wanted X while he works. Of course somethings may look like you are getting something yo do not want. But don't assume that it will end up like you want. Ask anyway "gee, this doesn't look like I want." A good worker will take the time to explain and will not think your stupid, ignorant of the work, yes, but then you hired them for their knowledge and skill thus they can't expect you to know that at this point of the job it looks like a total botch job when in fact it is only part of the process.
Inspect the job and the job site before you pay him. Some guys and some jobs require a partial payment of 10% at the beginning, 40 to 50% in the middle and the rest upon completion. In some areas this is a mandatory payment for all jobs, in other areas this is based upon a dollar amount of the whole job. Handing over a check means that you are satified with the work and that the job is Done.
That is for labor. Materials for jobs may need to be paid up front. This protects the Contractor who may end up buying a lot of stuff to discover that you didn't want it and he has to figure out what to do with a truck load of material.
I am a handyman, I do a lot of stuff, from basic rough carpentry, to masonry to plumbing. There are many things I will not touch - Plumbing older than 1970, electrical trouble shooting, big jobs requiring a lot of material hauling. I offer contracts, I also offer estimates not only for labor but material when applicable I make it clear who is paying for what, I even make it clear if I am getting the material or not. In many cases the client will get the material. If I come there to work and there is no material and we agreed that they would get it, I go to the next job. BUT I tell the client before hand that my time is money and if I come and there are no materials, I will go do something else. We, my client and I, work out the details BEFORE the job is started.
I am leery about taking on a job where the client insists that no contract is needed or wanted. I will not take some jobs because the client insists that they do not want a contract. Something is up, what, I don't know and I don't want to find out. Small jobs can have a hand shake agreement, clients who come by knowing someone else I will accept without contract, clients who have done work before no problem. Unless it is a big job.
I would expect the same kind of treatment in return. If I refused or didn't give you a contract something is wrong.
I make it clear up front that my estimates are based on what the job is assumed to be. There are many jobs which in the process of uncovering reveal other things which may not be covered by the estimate. If his happens I will bring out the client, show them what is going on and work out what will be done before continuing. Most contractors will halt the job for the littlest of things - Simply because it is wrong to assume that you want a thing done. Making assumptions in this kind of work makes for some big headaches. If a job stops its not because they are lazy, its because they are trying to do the right thing and make no assumption that you want something done.
I will not give out an estimate right then and there. Some people think that is a flag of warning; it is my reluctance to assume that the price of a 2x4 is still 2.35 per timber. It is because I want to sit down, write all the stuff, calculate it and give as accurate an estimate as possible. If a handyman throws out numbers right from the start I would be a little suspicious, handymen do all sorts of things. today they may be building a fence, tomorrow its painting, the day after than a sink repair - Prices for materials are always changing, no two jobs are exactly alike.
I also leave behind a clean work space. Many clients tell me to "not worry" about the saw dust that their gardener will get it later. I do not assume that they have a gardener, I do not assume it will be cleaned up later. But you should always err on the side of caution and make it clear if you want a clean work site left behind when they leave. If you don't, you may find yourself sweeping up sawdust, picking up trash and being aggravated because it is clearly obvious to you that this is part of the job.
Usually any problems I have on a job is the material, not the work. In a few cases there are issues with the work, but this is due to miscommunication. Thus the contract, estimates and the paperwork is there to insure that both of us understand each other and gives us a record of what we said. No paperwork means underhanded business practices and should be a flag of warning to you. Even if it is hand printed paper work, it is paper work, it is an attempt to get things clear before the job. None means something is wrong.
Some guys will insist on the partial installment payments on nearly all jobs - That is their right and in many places this is the law (Protects the contractor and the client at the same time). I would come to you and ask you at each installment "Is this what you want" and I would want you to look at the job in progress. That doesn't mean I am stupid or I forgot, I would be just checking with you in the process to make certain that that is what you want. It is far easier, cheaper and simpler to stop in the middle and take out half a wall than to find out at the end that the finished wall is not in the right place. Handing over a check is signing off saying "this is what I wanted" Or saying "This part of the job is complete" If you have any issues during the job, work them out and get them on paper before you hand over a check.
Communication between client and contractor is key to all sides being satisfied and happy with the job. A continual line of communication must be open at all phases of the job, and you need to feel ok with questioning everything, a question is never stupid, unless it is unasked and unanswered.
As a handyman my biggest issue with clients are those who call me up with only half an idea of what it is they want. I suggest you write out a list, so it is ten pages of things you want on a tile job - it is your right, you are paying for the work, you are expecting a certain outcome. Granted, maybe 8 pages are done automatically as part of the job, you can not assume anything automatically is done in any job. Assumptions make for bad jobs.
I hate to say this but handymen are the lowest form of low when it comes to work. I am a rare bird who believes that handymen are suppose to know a little of everything, are suppose to be cheaper because they work alone and are suppose to be just a little more friendly and helpful than a contractor because service is what makes the handyman a cherished service person, not the quantity of work or the that they are a specialist who does only one thing.
Used to be that your local handyman was called in for the small jobs, gave advise freely and was the first person you called to do the honey Do list things. Today many people call a handyman because he charges far less. There are many handymen out there who know squat, are out for the money and will screw you over if you give them the chance. Here in my home town there are a few drug users who will do half a job, insist on payment and disappear for a while or never return. It is a bitter pill to swallow, but many handymen are con artists.
I have a mobil home park of older people who through word of mouth get me a lot of work. All of them used to go to another guy who's work was far below my standards, and who charged way to much in my books and who, if I ever meet, may get a punch in the mouth. But then I have issues with robbing from the poor and elderly.
Thus If you do use a handyman, get one refereed to you by a friend. Failing that, Ask for references. I can hand you a list of 20 clients who will tell you I am a god of tools. If you need more than that I can get you more. Through the years I have made a name for myself, I have always asked clients for their name and phone number to use as a referral. I also hand them more than one business card and tell them that though I do run an ad in the newspaper, I give word of mouth customers priority over ad ones. (I rarely run the ad now days, I even scraped off the number and slogan off my truck because I get more than enough work through word of mouth)
Instead of asking "What can you do?" Ask instead "what won't you do?". A good handyman is one who will not touch certain things, the top ones are:
Old plumbing
Electric fixes (different than say changing an outlet or fixture)
re-roofing
Gas lines
Don't be afraid to ask why. In the case of old plumbing you may hear something along the lines of "Well old plumbing tends to break, and you end up chasing a leak" This is a truthful statement and reflects an experience or two. Older plumbing tends to be fickle. Another reason may be "Codes say" If a handyman starts off with that that means he is worth something because he knows local building codes.
Electrical may be along the lines of "I do not have the fault finding tools." or "That is really something I would refer you to a certified electrician for." This is what I do. I will switch out a light, a switch, an outlet. I will not try to find out why a breaker is being thrown all the time or why after changing the bulb, the fixture and switch your hall light still won't come on. This is usually indicative of a fault in the wire or a problem at the fuse/breaker box. Time to call an expert who can certify his work and has all the tools needed to find all the issues. (These tools are expensive BTW, and I already spent thousands of dollars on many other tools, each job needs its own kind of tool, can get mighty pricey)
Re-roofing "That is a hard job that requires a team effort/Expert/professionals." Big jobs, like an addition, or a total roof replacement, do require a team effort and in all cases also require a permit, building inspector to come out several times.
Gas lines "I really don't feel comfortable with working with gas, one minor leak can lead to big problems." Personally I don't touch gas. I am even reluctant to relight the furnace for new clients. Simply because I prefer to err on the side of caution and not risk sending up my client's house in a blaze of glory. Some handymen may know enough, or have the confidence in gas. Personally if I was a client I would call a specialist just because gas is dangerous.
Knowing their limitations means that they have a clear understanding of their skills. I have had a few potential clients drop me because I admitted there are things I will not do. That to me is irrational, especially if you want them to paint and ask about electrical and they tell you they don't touch electrical.
I think that is just about it, I tried to cover all points here. Sorry for the long post I'm in hopes I can spare you a few headaches along the way.
Cheers
David