Question about Federal reserve open market operations - reducing money supply
Have you ever gifted your parents a "I'll wash the house" ticket? Or maybe your parents just forced you to do it. In any case, money, or less colloquially a Federal Reserve note, is like a "I'll wash the house" ticket issued by the Federal Reserve. But instead of being able to redeem it for a house wash, you can redeem it to receive a certain amount of gold. That is if you lived pre-1971 (edit: pre-1933). Now you can't redeem it for anything, but it doesn't change the fact that Federal Reserve notes are a liability to the Federal Reserve. 

So if your parents cash-in your "I'll wash the house" ticket, what will you do with the physical ticket? Store it as a souvenir? Rip it up? Re-gift it? Sell it to them in exchange for a new computer? I think "[d]oes it even make a difference" sums it up pretty well, especially since most of the "tickets" are digital not physical.

Footnote: The government guarantees you can pay taxes with Federal Reserve notes. So in that circular sense, Federal Reserve notes are redeemable for something.