Yelp! I pulled out my bumper :(

The bumper needs to be lifted up and shoved in so that the visible loops go over the sort of hook things that hold it in place.

However...

Pull the black fender liner back a little next to and below the back upper edge of the bumper cover and you should see a bolt head, with the bolt pointing upwards. That is ultimately what keeps the bumper cover from popping out again. It is likely that your accident tore something there, and it looks like the place on the bumper cover where that vertical bolt is attached is missing. That fragment is probably still in there, still held by that bolt. There is also a bolt on the bottom rear corner, which comes up from underneath the car.

Watch this video, 4:44 for the top bolt, 2:59 for the bottom bolt:

Note, if you start messing with the fender liner and bumper cover you will break an assortment of fasteners. That old plastic becomes very fragile with age.