The fed doesn't gift money to anyone. To decrease money supply, all they have to do is reduce the amounts of reserves available to banks and sell back the bonds they have been buying feverishly and wait for any remaining loans to come due.

Now the government can gift money, but they must either use tax revenues and/or borrow by selling treasury bills - which can be to the public or the fed can buy them - but in either case, they must be paid back.