Despite brake service we are experiencing rear brake squeal while backing up in reverse. Any solutions would be welcomed.

Welcome to NICO!
Typically brake squeal is attributed to either the shims on the back of the pads, or lack of (or improper) grease on the back of them. Grease (or other specialty substances) is often put on the back of the pad (between the pad and the caliper) to act as a damper and stop squeal.
Did you do the service yourself, or did you take it somewhere?

Thank You.
We had it serviced and have since moved out of state from where it was serviced.