Resolving "partially paid"status after capturing a discounted price

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A customer made several purchases with the store and asked for a discount on shipping. We agreed to $15 off the cost of shipping and we applied the discount by capturing $15 less than we were allowed on the customer's credit card. (Eg/ Item and shipping were $200, we captured $185 from their card). Now I have a bookkeeping problem because this order has only been 'partially paid'.

How can I apply a post-payment discount so that we can clear the partial payment?