If not, one approach would be to cancel the card and walk away.
That doesn't work. You are still responsible for any charges on the card prior to cancelling it. Pre-booked, discount reservations with a no-cancellation policy are generally charged at time of booking.
The OP might have been confused when reserving because entering a credit card is standard for placing a "hold" on the room. That may have been what they thought they were doing. But it seems maybe they later realized it was an actual, pre-paid booking (and likely with a no-cancellation policy).