@Account Closed
Credit cards don't bounce six months after the fact. The transactions are authorized in real time and batch processed at night. If your PM is saying it "bounced," well I'm not surprised that you and they are in this situation.
If the more-likely scenario of a "chargeback" occurred, then you need to write a letter to the PM asking that they provide, within x number of business days,
a) the initial chargeback notice from the card processor, which must state the date of the chargeback, the reason for the chargeback, and the date given by the processor as the deadline to respond to the chargeback.
b) Any documented attempts to resolve this with the tenant outside of the chargeback process, once the chargeback is initiated and prior to the deadline given by the card processor to respond to the chargeback. This is possible, as the tenant/requestor can rescind the chargeback.
c) Any documented attempts to further resolve this with the tenant after the chargeback was completed (meaning the card processor either denied the PM's response, or the PM didn't respond in time) and prior to their contacting you to request that you pay them "back." One assumes that even if the tenant won the chargeback, the rent was still due. The PM's responsibility to you is collect that rent, regardless of whether the initial payment was made with bad money (which could be a declined credit card, a bounced check, or even a counterfeit bill.)
My suspicion is that the PM will not be able to provide these documents, and is hoping that you will just pay what they say you own them. I believe it is well within your rights to request this simple documentation, as your agent/PM's primary responsibility is to collect and disburse your rents.
Good luck. We'll all be eager to know what happens next, I'm sure.