Yes! If you have a Grommet account, you can absolutely save a credit card on file.
Cards can only be saved to an existing account and only during a transaction.
Log in to your account and in the "Payment" section of Checkout, there's a small box underneath the credit card form that says "Save for Future Use". Click on that box and then "Continue to Review". Once you place the order by clicking "Place Order", your card will be saved for the next time you shop with us!