Indeed, Mozart. Here 'the Duke of Marlborough' would always mean the famous Duke of Marlborough, who happens to be the first Duke: we don't use the numbers unless there's a risk of confusion between the current Duke, Earl or whatever and the historic bearer of the title or, of course, a pub called the same.

('The Duke of Westminster' always means the current one because he has
no famous predecessor

He's the sixth Duke but surely nobody, apart from Gerald Grosvenor himself, has ever heard of the others)
As to Harriet being a granddaughter, that puzzled me too. If she's a granddaughter what's happened to her father, the man who would be offering a dowry? And I can't find any granddaughter, Harriet, of the great man , on the family tree.
'Granddaughter' comes from the Daily Mail's review of the book 'The Kit Kat Club' by Ophelia Field, which gives the story.The word may be a typo in the review
Anyway it doesn't spoil the story if Harriet, the daughter is intended.Let's read it as her case.It's an amusing , if British, tale.

Have a go!