I believe you should contest the chargeback. They have authorized the transaction then they should pay for it.
The reason you got the chargeback is because the original cardholder complained about the transaction, not knowing that his/her card information has been compromised. Automatically, they charge it back to the merchant. The settlement should be between the cardholder and the card company. If the cardholder was proven to be careless with their use of the card then he/she pays for the transaction, if not then that's the time the card company will shoulder the amount as a loss.