Just log in to your student account and head to your dashboard. In the top left corner of the page, you'll see a section that reads Payment Information, preceded by a checkmark. To the right of this is an Edit link. Click the link to go to your Wyzant Wallet.
There you will find the payment method(s) you currently have on file. Just click Remove for any method you want to remove from your account.
Please note that in order to continue messaging with tutors, as well as scheduling lessons, you will need to replace the payment method you removed with another valid method of payment.