Refunding customers acquired through affiliates

I am looking to understand how I can refund customers direct who were acquired through an affiliate. The proposed payment mechanism from th affiliate is direct onto the customers credit card - the one used to sign up originally. This is  difficult for my organisation; our preferred route, would be to pay the affiliate and they manage payment to the customers. This was rebuffed on the grounds; the affiliate would be required to do additional tracking to locate customers.

In essence I am asking what is a viable mechanism for refunding customers without going through the card payment provider - do payment processers, like Cybersource offer this service - so the money would get back to the customer as a refund would.

Any advice would be helpful.

Sonu.