Question about Federal reserve open market operations - reducing money supply I'm trying to understand how open market operations work to reduce money supply.

So the Federal Reserve sells bonds... when this happens, the bank balances of the bond-purchasers goes down... the bank balance of the Federal reserve goes up.

So now what does the Federal reserve do with this money... is the money just eliminated from the system completely? Or does the Federal Reserve hold that money? Does it even make a difference... Thanks.
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.