I had a similar issue.
A buyer (with a rather poor feedback rating over many transactions from other sellers) purchased a pendant from me. She sent me a convo explaining that it was chipped on the back, so I asked her to send a picture so I could assess the damage and we could work out a plan for a refund/replacement if necessary.
She sent a pic, two days later, of the front. No pic of the supposedly broken backside. That (along with her poor feedback score, which had worried me from the start) gave me a good hint at where things were going. I asked her for a picture of the back, naturally. She gave reasons why she absolutely could not do that, and assured me I was irresponsible and rude for questioning her. So I just had her send it back and I gave her a refund. I didn't want to risk getting a negative (this was one of my first sales, which meant a negative would have made my feedback rating about 67% positive. Eek!).
Anyhow, she sent the pendant over a week after she said she would, poorly packaged with no padding whatsoever. I think she was hoping it would break on the way? Well it didn't. It was not chipped in any way but I just gave her a refund and deleted the transaction to get things over with. I sold the piece at a Craft Show a few weeks ago to a very happy customer. :)
I don't know why I posted that exactly, but even though the customer was frustrating, I maintained good customer service throughout the transaction and ultimately made her happ...well, a little less angry! This was the route I personally chose to take. I avoided negative feedback (still have a 100% positive rating!). I figured that if the product was really broken, then a refund would be in check, and if it wasn't I could resell it and at least break even on the piece. I think it was a good choice for me. What you do is up to you!