Is it possible to completely remove my current credit card information from my account subscription?
Credit card information can be removed from your account if you switch to another payment method to pay for your subscription. Otherwise, if you pay for your account subscription by credit card, you will not be able to manually remove all credit card information from your account. You can replace your current card's details with those of another credit card, however, if you pay by card, there will always need to be a card in place on your account.
For more information on how to update your credit card details and switch your payment method, see the articles: How can I change the credit card on file for my account? [Video] and Managing payments.