I want to mail a check as a payment method.
Hi, here is an Apple Support article on how to make payments on your Apple Card account,
Pay by mail is not an option in the article. At the bottom of the article is a link to Apple Support if you have issues linking your bank account, or making a payment etc.
I know this isn’t the option you were looking for. I would strongly urge you to make contact ASAP through the link in the article. I hope this helps.