From the factory, the plate holder is riveted on with 4 aluminum rivets - If a dealer installed it, they probably used the same thing because the factory kit comes with the rivets and the installation instructions are on the bracket. The heads of the rivets are HUGE, but the holes in the front fascia are actually quite small - 5.5 mm (7/32nds) is the size they tell you to drill if you're installing the factory part yourself . . . . and just the top two holes would be plenty - 4 rivets is way over-kill, IMO
The 'secret' to removing Pop rivets is to carefully drill with a larger drill bit (3/8ths or so works well for these) just enough to get the head of the rivet to come off the shank and then you can push the remainder of it through the hole so it will fall out the back. It's pretty likely that the rivet will begin to spin before the head falls off, but you don't actually need to drill it all the way off - You can pop the head off with a small flat screwdriver if you've drilled it deeply enough. If not, use the screwdriver to keep it from spinning so you can drill just a little deeper. The aluminum is very soft and drills easily - Just be careful to stop when the head comes off
This method will leave you with a hole no larger than the original one drilled in the car. I did this yesterday and the holes aren't really noticeable at all. I am eventually going to fill them, likely with a bit of epoxy and then paint it to match the silver of the fascia, but for now it looks OK with just the holes
Don