Admins can delete a credit card by navigating to the Admin module on the main left vertical pane, and then to the Billing primary tab on the horizontal menu. All credit cards are listed under the Payment Method section. For instances where there is more than one card, there will be a Delete button for each card with an exception to the default payment card.
To delete the current payment card, another card will need to be chosen as the default payment card first. If there is only one credit card listed, the option to delete will not be available. Another card must first be added and selected as the new default payment card.