Why is my customer claiming that they were charged for a declined transaction?

Answer: When a card issuing bank receives an authorization request for a charge, they will confirm that the card number is valid and verify that there are available funds to cover the requested amount. If the funds are available, the card issuing bank will reserve the funds, and return an authorization code that allows you to claim the funds during settlement.
 

If you are using the Address Verification Service (AVS), the card issuing bank also compares the cardholder's billing address on file to the address submitted with the transaction. The bank then returns an AVS response code along with the authorization code that indicates whether or not the billing address matches the bank's records. As the merchant, you decide whether or not to accept the transaction based on the AVS response code. If you choose to decline transactions that return a certain AVS code, any transaction that is returned by the card issuing bank with that AVS response will be marked as Declined and will not be settled.
 

However, even if a transaction is declined due to an AVS Mismatch, the authorization code and the hold on the authorized funds will remain on the customer's card until the card issuing bank removes the authorization. As a result, the held funds may be subtracted from the customer's available balance, and an online statement may show the authorization request, which might be mistaken for an actual charge. Most card issuing banks will remove authorizations within 3-7 days if they are not claimed for settlement

*Note: Although you may request an expedited release of funds, it is ultimately up to the bank whether or not they will do so.