Making a customer refund creates a different transaction in the Customer's profile. You can unlink the credit card payment in the invoice and then apply the check payment.
Here's how to do it:
You can now apply the check payment in the invoice, just click Receive payment.
After that, you can delete the unapplied credit card transaction. Here's how:
You might want to check out this helpful article: Enter and apply a credit memo or delayed credit.
If you have additional questions, feel free to swing by anytime.