How I can Remove Member Organization with error code ConstraintViolationException (The member account must be configured with a valid payment method, such as a credit card.)?

If you do not have access to email account, you can try the option of closing account via AWS organisation and then removing it. I have tested this by creating and closing the account via AWS Organisation. You will have to wait for post closure period to end and account should be removed ((please see note section at the end)

Go to AWS Organisation of management account. Click on the account link you want and then on the right side you will see the close option. Clicking on the Close button will close your account.

Note: When you close a member account, that account isn't removed from the organization until after the post-closure period. During the post-closure period, a closed member account still counts toward your quota of accounts in the organization.

https://docs.aws.amazon.com/organizations/latest/userguide/orgs_manage_accounts_close.html

Though I used valid email to add account in the organisation, but I did not access the email at all. So I am assuming, you should be able to close account (and finally remove it after post closure period).

Also to note, you will still get the same error, if you try to remove the account manually after closing it during the post closure period which is 90 days. Closed accounts are visible in your organization with the SUSPENDED state until 90 days and after that they are no longer visible in your organization.

Please let me know if this worked for you, in case you chose to try this option.