Start with the fact that they are ignorant and things will be a bit more clear to you.
This is your customer's issue, but if you want to be helpful write your customer a letter recapping the fact situation and how it was resolved much as you did here. If your customer wants to send the credit union a copy of your letter as an explanation that's up to them.
I'm resisting my compulsion to draft a cover letter for your customer...I would enjoy it immensely. P.S. Before you get too feisty at my recommendation, look at the item as returned and note the reason you gave for returning it.