AITA for not refunding a customer for "fraudulent" purchase?

NTA. Definitely sounds like she's trying to scam you. Most people don't reach out to the merchant for fraudulent charges. You're supposed to call the bank and deactivate your card and they'll take care of crediting you for those charges.

I'd suggest having her file a dispute with her bank. They'll conduct their own investigation and credit her if she's right. If a billing address was entered they can check if there was an Address Verification Failure or not, which could indicate a compromised card. If the AVS matches, then it would confirm she did the transaction. Same with the CVV2 code on the card. If she has the card in her possession and has authorized no one to use it, with the CVV2 and AVS matching it would confirm she made the transaction.

/r/AmItheAsshole Thread