How to Handle this Parking Lot Incident

We were backing out of a parking spot, apparently at the same time the car behind us did the same thing.
We both have damage on the very corners of our bumpers.

The other guy called the Sheriff to come out to the parking lot, but they wouldn't do so. So we exchanged insurance and driver license information and both said "Have a nice day". No one really talked otherwise.
Realized after the fact that neither of us exchanged phone numbers, nor did either of us take pictures (unless he did and we aren't aware).

The damage seems minimal, on both vehicles. I don't intend to do a claim on m
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