I find thank-you notes horribly difficult to write for some reason, especially when the gift is not well-aimed (which is... usually, to be honest). I often end up skimming through 10-20 sample notes online before I can grind something out. Anything to make that process easier would be worth considering.
(This is honestly the first time I've seen a personally useful application for this tech.)
Why are you thanking someone for a gift? Because they thought of you and went out of your way to get you something, and you appreciate them doing that.
So just say that.
You would probably enjoy Bureaucrats and How to Annoy Them[1] by R.T. Fishall, a nom de plume of Patrick Moore (of xylophone fame [2], maybe some astronomy too).
[1]: https://www.goodreads.com/en/book/show/4416489-bureaucrats-h...
It was quite good, especially after a followup prompt "Not confusing enough. Make it more confusing.". But of course I didn't send it in the end.
I find the act of getting an AI to write this kind of thing for me to be deeply entertaining.
So even if I could have written the letter myself, I would much rather do it like this instead.