GloryBells • 
Feedback is the buyer’s opinion of the overall transaction. As long as it doesn’t violate policy (the one left for you doesn’t), eBay will allow it to stand.
ebay themselves don’t consider feedback when evaluating sellers, so there’s no concern there.
I just read the feed back shown on your account here. Am I missing something? Was this for a Tarzan item?
From what the feed back said, they were expecting a partial refund? Did you communicate with the buyer before they left the feed back?
If you are to give a partial refund, you do that right from eBay. Not sure why you would send a check? I'm sure your funds are probable pending due to not selling in a while and that made you think you had to wait, but they will get released eventually and the partial refund comes out of that.
It can be difficult to always do the right thing as a seller, I know this myself. And sometimes buyers can be difficult too. But as sellers we need to try to do the right thing, answer promptly and do what we tell the buyer we are going to do as promptly too.
At this point, all you can do is make sure they get their partial refund if you agreed to one, and apologize for the trouble. And if you ask nice enough, you could try to have them do a feed back revision for your account. (You have to make the request for that)
But take care of the problem first. Good luck!
