Buyer falsely claiming item is fake
Buyer purchased a bag from me and waited over a week to reach out to me to complain. She falsely claimed the item is fake with no proof and demanded a refund. The bag is in fact not fake, I purchased it directly from the retailer. I initially was going to just have her return the bag to me (even though I don’t accept refunds and the bag is real) until I realized she left negative feedback before even giving me a chance to respond to her message (I responded to her within 3 hours!) I then checked her feedback as a buyer and saw she’s done the same thing to other sellers, made false claims about fakes and demanding refund. I told her she’d have to go through eBay now to try to get a refund that I’m not accepting a return based on her allegations the bag is fake when in fact it is authentic and I didn’t appreciate a negative review that she left before I even responded to her 3 hours later. Did I handle this okay. Should I have done something differently or is there anything else I can do?