Go to the customer's profile->billing information->payment accounts.
There should be a red "delete" button next to the credit card.
If you don't see a "delete" button next to the credit card, the credit card account is selected for Autopay. You will need to remove it from auto pay before deleting the card. You do that from the blue edit button on the right side of "Billing Information" as shown in the screen shot below.
