Legal Question in Insurance Law in Georgia

You left out an important detail. How was the car damaged? Was it their fault or an act of God (like weather) or something else? If they are at fault, you could sue them if they refused to pay. If it was, let's say, a hailstorm, or a tree falling on it, probably you bear that cost. However, it is possible they actually have insurance that covers the damage, and most reputable mechanics would probably offer to pay.