You're welcome, @tabradley.

Thank you for sharing with us more information about this refund transaction.

For recording purposes in QuickBooks Desktop (QBDT), you can choose to keep the credit memo you've created and then apply it to cash or check. From here, you can get rid of the transaction showing as a credit card refund. 

Here's how you can give your customer a credit or refund in QuickBooks Desktop for Windows to select how you're going to handle the credit based on your situation. 

Check the following information on how you can run a report showing customer payments you have received, invoices, and deposits to which the payments are linked: Customize customer, job, and sales reports in QuickBooks Desktop. 

Let me know if you need further help or information about recording a credit card refund. I'm always glad to help. Have a great rest of the day!