At first glance, my brain screams, take the money. After some reading, and the inevitable post of "what if it were you" I'm left with the same end conclusion but much less conviction.
There is notable damage to your vehicle, as noted by the 2 estimates. Yes, you fixed the damage enough to appease yourself, but when the day comes that you want to sell the car or trade it that damage still remains. Consider it as an investment toward a future loss. Or a current loss with a future price tag. It doesn't effect you now, but at some point, it will change the value of your investment.
Now the small voice in my head is whispering that the guy who sent you the 1600$ out of the kindness of his heart for you to do little to nothing related to the reason the money was sent should be considered. If you send the money back to him, the game of paying it forward begins. He gets this check in the mail, he is pleased and surprised, 1600$ while not being an extravagant amount of money, is still a sizable sum. In essence the good deed that he did(he REALLY didn't have to do this), repaid by the good deed that you are thinking of doing will in turn cause other good deeds to snowball down the mountain. In both his case and yours and possibly a certain amount of readers of this forum.
Regardless I'd keep the money, and I vote ethical. This 1600$ will come back to being relevant at some point even though currently the solution is acceptable.