Glad to have you join the Community. I'd be happy to share info about deleting a customer's credit card info.
To do this, please follow the steps below:
1. From the left menu, select Sales, then Customers.
2. Choose the customer you want to edit.
3. Select Edit in the upper right.
4. Go to the Payment and billing tab.
5. Choose a default payment method then select Save
Give this a try and let me know how you make out. I'll be here in case you have questions.