mine looks like its held on by 4 screws with triangle slots for the screwdriver. I can't find anything to work. And I'd rather have a couple holes then the holder that I don't use.
It is held on by rivets. You can use something like a 1/4 inch bit to drill the center out of them. When you're done you can plug the holes with body panel retainers, available at any auto parts store.
I put my work vehicle (2008 Dodge Charger) in reverse while parked 6" in front of my brand new Sonic. 5 seconds later, and TaDAAA! No more front license plate holder. LOL. I would go with River Rat's advice though. It is much cleaner looking in the end.
If you don't like the holes, then try partsgeek.com. I ordered the lower grill portion from them and if I remember correctly it was $42 shipped. Direct replacement for the one I broke, and no mounting holes for front LP.
To do it the correct way the bumper has to come off. The grill has about 8 to 10 tabs which must be tilted/pried as the grill is pulled out the front of the bumper. Some of them are pretty strong, and I believe the bumper beam would block you from getting a good angle on the top tabs of the lower grill.