From CRM > Customers you can delete the card on file for a customer if you have administrator or reservationist permission levels in Xola.
Simply expand the customer record by clicking the blue + and click Cards. Then you will have the option to delete the card on file. When a card is deleted you can still refund to this card, but you cannot charge the card without re-inputting the information.
Xola will automatically record which logged in user deletes a card on file in the Customer Notes section of the customer record. If you don't see this immediately try refreshing your page.