How do I remove or expire an active coupon from a customer’s account?

You'll want to first visit the customer's account page within the Recurly application and from there, you can find the "Manage Coupons" button listed both under the Account Information section, and if you scroll down to the Coupons Overview, you'll find it there as well, please click that button to be brought to the next coupons page. From there, simply hover your mouse above the coupon redeemed on the customer's account and click on "Remove". Doing this will remove the currently active coupon on the customer's account and mark it as expired.

Similar behavior can also be done through the developer API by using the following API call:

https://dev.recurly.com/docs/remove-a-coupon-from-an-account