This reminds me of a service I signed up for once years ago, can't even remember what it was, but I had no idea how to cancel it and it was direct to my card instead of PayPal.
What ended up happening was I went to the "Edit payment info" page and just entered my card number as 4242 4242 4242 4242, which is a Visa testing card number.
It authorized it as valid and I never dealt with the company again.