Admins can choose a credit card by navigating to the Admin module on the main left vertical pane, and then to the Payment secondary tab in the Billing primary tab. If there are multiple credit cards, a different card can be chosen by clicking on the desired one. The default card will be indicated by the highlighted selection dot on the left side of the credit card line.
Note that the credit card currently being highlighted as the default payment card will not have the option to be deleted. Another card will need to be chosen as the default payment card first.