We don't store your CC information on our servers at all. The bank we use sends us a token, sort of like a codename for your card specifically, that they use to represent you.
The only thing we do keep on file is the last four digits of your card just in case we need to keep track of charges, sort of like how the last four digits of your card get printed on a credit card receipt.
While we have no actual credit card information on our site to delete, you can prevent charges from being made on your card by either switching to a new card, or turning all auto-renewals on active subscriptions to "OFF".
Looking to avoid charges? If all the subscriptions are cancelled, there won’t be any charges. You can click the "cancel subscriptions" tab on the left hand menu to manage your subscriptions. For specific instructions on canceling your renewals, please check Cancel My Subscriptions in the Help section!