The lesson is not odd. I am English. Before my retirement I was a teacher and taught English grammar for many years. The pluperfect may not be used often, in English, but it is grammatically correct, a valid tense (as in French) and is good English. American English is a different language. It would be impossible for the site to provide for the differences between American and English English.
As Aurelie said, in spoken English it would have been "I'd had...." with the apostrophe replacing the "ha" in had, but it still means "I had had....."
It's true that there are differences between American English and British English, but I don't think this is one of them. I'm a native speaker of American English and the pluperfect in that language feels perfectly natural to me, both in speech and on the page. Besides if it's used in French, we want to learn it, don't we?
Today when reading Gruff's response to Alan I just had to respond but I had to reread the material. Yesterday I had not yet read it but I had had to read something else before then.
Now I'm convinced I may never have to use this verb tense again.
Oh! I just now remembered that yesterday I had to take an exam. Before I could take the exam I had had to read something just as difficult. Now I'm sure it wouldn't have mattered if I were American nor British, I would have had had to do the same.
There is a Big Bang Theory episode where they get tripped up over a time traveller being future past plu imperfect or something like this...
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