The garage can only claim storage and recovery fees from the owner of the car.This could be you or the insurance company,depending which way the setlment has gone. If the insurance have paid out they are the legal owners,unless you agreed a retension clause when you insured.
You are right, but this in theory, but when i write of mine long time ago, the garage start to claim more, like time spend in investigation etc etc , i have to fight for take back the remain and don't paid, but that paid off for me an other garage give me 30% more for the remain.
But my car be less than a year and the price much more than a Mog