I don’t quite understand the “No fault Accident “ bit......I have always been led to believe that if you are reversing and hit something it is always your fault.
I had a similar incident a year or so ago when a Mercedes reversed into my nearside front bumper, my local body shop did the job for £60.00 and the other driver paid up the cost.
I would get another quote from a local paint shop because as we all know if you had a transmission solenoid fail and took it to Lexus they would quote for a completely new transmission.