When your client is paying securely through Stripe they will have the option of saving the card they are using for payment with your company.
If your client selects this option you will be able to used their saved card when you look under 'Billing' and 'Capture Payment'.
You will be able to push a charge to one of their saved cards by clicking 'Saved Cards' on any project.
If your client didn't opt to keep their card on file, you can still push a charge to the credit card that they used for a previous payment on this project. Note that Previously Used Methods won't be available across all projects, but Saved Cards will!
You can also see any Saved Cards when viewing your client's information under their 'Billing' section