In this case the bumper was knocked off / destroyed, which means they need to replace the bumper (this appears to be the only viable repair). Thus they will pay to have this done. The previous minor damage would not change the need for this being the repair.
Rear bumper replacement costs can range from a few hundred dollars for a bumper up to $10,000 or more if the frame of your car is bent
My choice for personal transportation is another route in itself. A Human Powered Vehicle requires a different approach to planning one's route. The roads we take can often turn out to be the ideal alternative to taking the primary roads.
Simply loosen your bumper screws using a screwdriver, pop the bumper and gently pull it out, then push the front bumper forward so you can access what needs to be replaced.That way, you can be sure that when you pop your bumper back into place, it's going to be held by brand new clips on both sides.
Even if you've been involved in only a minor collision, it is extremely important to have your bumpers repaired as soon as you can. It is best not to continue driving your vehicle with damage to some of the bumpers, for the simple reason that it is those bumpers that could help save your life one day.