Eliminating a payment method is very easy; you just must click on the delete button next to the payment method in the Billing data section.
STEP 1. Open your Settings menu and choose "Billing data" from the dropdown menu.
STEP 2. Choose the payment method you want to delete and click on the delete button.
However, if it happens that you have only one payment method and for some reason, you want to delete it, you must take into consideration that it is not possible to eliminate a payment method which is saved as a default method.
Therefore if you really need to delete this payment method, you first must add another one and make it your active payment method so that the delete option would become active next to the first payment method. In case you are interested in how to add a payment method, you'll find the information HERE.