Giving them access to your account or credit card is a bit wild. That's what prepaid cards are for. You charge it with exact amount of money you need to pay for what you want and leave it empty after you pay. You can later watch for bounced payment request to help evaluate their reputation. At this point Anthropic is about as reputable as shady porn site.
See also: privacy.com
(Virtual card provider that generates cards as a free-to-the-user service. They make their money from a cut of the standard transaction fees. Cards are locked to a single merchant and it’s easy to configure limits.)