Keep in mind that the refund may not be all that's at stake - in some cases I've seen customers worth tens of thousands of dollars in repeat business in the future who threaten to leave if they don't get their way. In fact, it may be that it took so long because the customer finally came back and said, "I want to submit this invoice, but I won't until you fix my perceived problem." and the company then had to decide between you and the customer.
It's not nice, but that's capitalism for you.
In a right to work state they can fire you, but they will be on the hook for unemployment unless they can prove to the state that you fit within the very narrow limits for termination without unemployment insurance. So go apply for unemployment, and fight them for it if they submit to your AG that you are not eligible. Especially if you followed the correct (at the time) procedure and process for denying the refund, and certainly if you did not have a manager on site that could handle the customer when the customer asked for one.