Can an external terminal solve gift receipt return issues?

[BundleYourJoy]

So our store has a policy where customers can return and exchange items within 14 of purchase with the gift receipt. But recently a customer wanted to return something that she didn't pay for, hence the gift receipt, but Shopify dos not allow us to put money back on a card that was not used to purchase the item. Neither can we issue her cash. It has to be the same credit/debit card. Is the only way to solve this problem to switch to an external terminal? Since the external terminal would allow us to put money back on any card, regardless of which one paid for the item initially.