The way that my bracket was mounted was with plastic clips that have a pin in the center to expand the clip. I don't know if that's how they all are, or just how this dealer did it. If yours are like this, you just push in the center pin, but it goes all the way through the clip before it gets loose enough to take it off. So I had to take the grille off to get the pins back out of there. There are only 4 screws holding the grille and black part of the bumper though, so it's easy.
Also, the holes that it left were pretty big, so I just got a new grille. I think it's around 130-140 dollars.