If you need to remove a redemption from a customer's account, you can do so through the Recurly UI or the API. Visit the account and click on Manage Coupons in the Account Information module or above the Coupon Redemptions table lower on the account page. Manage Coupons will take you to the Coupons Redemptions page for the account where you can select the redemption you want to remove from the Redeemed on Account table. You will find the Remove action in the right hover actions for the table row.
If you only allow one active coupon on an account, you can also remove an existing coupon redemption by redeeming a new coupon. When accounts are limited to one active redemption at a time, redeeming a new coupon will automatically remove the existing coupon and then redeem the new one.