Forgive me for not taking pictures of the removal process.
1. Examine how bracket is attached to your car. Mine was attached with rivets. I believe some may be attached with bolts?
2. Get yourself a drill and 2 drill bits. One should be slightly larger than the inner tube of the rivet and the other about 3/4 the diameter of the larger outer part of rivet head.
3. Drill with the smaller bit straight through the rivet shank. If the rivet spins (not likely at this point) then try and hold it down with a flat-head screwdriver.
4. Switch to your large drill bit. Now drill off the head of the rivet. This time you'll almost certainly have to use a flat-head screwdriver to keep the whole rivet from spinning.
5. At this point, you should be able to pull the bracket off completely.
6. Reach your arm under and up to try and retrieve the back end of the rivets. Or just push them in from the outside and don't collect them.
7. Plugging the holes. If your bracket was attached with rivets, the holes should be relatively small, about a 1/4" or less. Mine were fairly small. I know that members here have used bumper plugs but I thought they were too expensive so I went to Home Depot.
8. Measure how big the holes are in the front. I used a pencil point poked in and noted where it came to... (sorry, no calipers at home haha)
9. Go to the hardware section of Home Depot (or a hardware store). NOT the cabinet knobs and hinges "hardware" aisle, but the nuts, bolts, etc. hardware one.
10. I found my plugs in a drawer mixed in with the nuts and bolts. It was in a drawer labeled "Hole Plugs".
11. Select a plastic snap-in plug that is slightly larger than whatever your holes measured. There were also zinc plated steel covers but I went with the plastic as I figured they'd be easier to paint but you can pick whatever you want.
12. Once back at home (or in my case, the HD parking lot...) get yourself another drill bit that is about 1/16" smaller (possibly 1/32" smaller) than the size of plug you bought. Mine were 1/4" plugs. Drill your holes in the bumper with the bit.
13. Pop in your plugs! At this point, you can paint them to match or I guess paint them prior to pushing them in. Walla! No plate holder with plugs!
Below are some pictures of how big my 1/4" plugs look. Sorry I haven't painted them yet, but that'll come soon. They appear to look a lot smaller than some of the others used based on posted pictures from other users.
Here's the bag that mine were in if you need help finding these things:
Picture of the cap. It's got a lot smaller head from what I can tell vs. other caps.
Measuring tape, I mean... Pencil eraser for size.
Pics of the front, sorry they aren't painted yet:
So yeah, I hope that helps some of you that are in the boat I was... aka couldn't find these "plugs" in the hardware stores. Now you've got an SKU and hopefully decent description of the location of them!