If the merchant realizes that they were on the losing end of a chargeback and also issued a refund to the customer, they can represent the chargeback, but only if they are within the VISA/MC timeframes to do so.
VISA/MC permit the merchant to send a "good faith collection letter" to an issuer requesting a refund of the overpayment. To Randy's point, that doesn't mean that you have to honor it and I wouldn't do so without the customer's consent to debit their account.
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