I am facing a grating noise problem whenever i start my car and am just about to put it in drive/reverse. It doesnt occur at driving speed, but just as the car is about to start. It is a grating noise, probably from the back side of the car, maybe the differential.

Firestone suggested me to change the seals on the rear differential output shafts. And most of the normal mechanic shops wont do it. Audi of Danbury charges me 109(per hour)*3 (hours) dollars for it. Thats a cool 320 bucks. And this without the seal charges (Dont know how much that would cost)

Any idea how this problem can be solved? In any case, there is no visible leakage of the differential fluid.

Car details
Audi A4Q 2.8L 1998 model

PS: A local mechanic agreed to do this for 120 bucks. Should this offer be taken?