How to remove a discount code from a customer's membership

Go to Discount Codes and click on your desired discount code:

You will then be able to see a list of customers who have used the code, and what they have used it for.
Click on the customer name, and this will take you to the customer profile page:

From the customer profile, click on the membership tab.

From here select the membership you would like to remove the discount code from:

This takes you to the detail page for your chosen customer membership.
Click 'Remove Discount':

And now confirm you want to remove the discount:

The discount has now been removed from the customer's membership, and all future payments.