Q: Delete credit card information on my account.

You can try this support document for instructions on editing your payment method.  Change or remove your Apple ID payment information - Apple Support

However, you may not be able to select None, and if not, this explains it. Why can’t I select None when I edit my Apple ID payment information? - Apple Support

Hi,

You posted in the Setting Up Apple Pay community so if you are trying to delete a card from the Wallet follow the instructions in the support article >  iCloud: Remove credit and debit cards from Wallet (or Passbook)