You need to provide the best customer service that you feel comfortable doing. eBay encourages sellers to provide great customer service.
At this point one needs to make a business decision and not an emotional one.
IF there was something in your listing pictures that was not part of the listing then this ripe for a SNAD claim. First, I'd try to figure out how that happened and correct it going forward with your listings. Also there is an issue of a dead battery. Next recognize that one has an angry buyer and a SNAD case is likely - so it appears as though one is in the position where they are going to lose money - what decisions one makes determines how much money one will lose.
One professional approach is to write:
Dear Buyer,
I am so sorry you are not happy with the _______ and that it does not meet your expectations. Please return the item and when we receive it we will be happy to give a full refund.
Seller
So in this approach perhaps the buyer pays for return shipping, OR one can offer to send a label. Your loss in this situation will be the two shipping charges.
On the other hand one "could" offer the buyer a partial refund of some amount that is less than the return shipping, IF one thinks that could end this and make the buyer happy. This is the "lose as little as possible" theory. I guess also, with this theory, one could do as you suggested send the accessory to the buyer. The risk I guess with that is that the buyer eventually files a return and keeps the accessory, since it was a "gift" and not part of the listing.
Then again, this buyer sounds a bit unhinged and unreasonable. So one could think about IF they want to jump through hoops just to avoid negative feedback? Those red donuts age off one's account after a year in the calculation of the FB %. If the buyer has threatened negative FB if you do XYZ, then perfect, one can proceed without worry as that FB could be removed under the extortion policy.
There is no clear cut answer as to what one should do and no one has "the" right answer! Weigh the facts and use your personal level of risk tolerance, etc. and make a business decision.
Good luck!
