Yeah, that gift while arguable from the American People, was paid for by President Obama.
I'm glad the Queen liked the Broach the Obama's got her from a small shop here in D.C., better than the ipod filled with President Obama's speeches gifted to her by the first family on the occasion of her 90th birthday in 2016. Before you turn your nose up at that, don't forget Gordon Brown the then British PM got a 25 set gift pack of Movie Theme CD's from the Obama's in 2009, which I believe I saw at Costco around the same time. And that's the Gifts given to the leaders of Britain arguable America's strongest most reliable ally!!!
Seriously though, Presidential Gifts, and entertaining; like state dinners and such; all come out of the President's own pocket. It's one reason most American Presidents leave office in extreme debt. U.S. Presidential gifts are thus notoriously cheap, the Obama's were not the exception to the rule, they basically were following the rules. Before you feel sorry for American Presidents, the debt for modern Presidents as you can imagine is temporary. As Former Presidents do extremely well financially with speaking and book fees. Also they can draw salaries from libraries and charity foundations they work with not to mention the permanent salary they receive for the rest of their lives from the American People. We are not even discussing influencing peddling and a sort of unofficial lobbying which some Presidents also take part in. (Cough Cough, Bush Senior, Cough Carlyle Group, Cough Cough )..
It's an odd sort of duality all gifts accepted by an American President are accepted on behalf of the American People. Any gift with a worth greater than $50 per event or $390 annually. Gifts greater than this must be declared, and eventually turned over to the Government. (Amy Carter's baby elephant ended up on the zoo).
This is especially odd because if you wanted to give an American Politician 100 million dollars cash anonymously, that would be perfectly legal as long as you ran it through one of his, or his parties political action groups. America is a whacky place.