The first step is to mark where the license plate frame hits the bottom of the backing plate. I didn't have a pen that would mark the black plastic so I took a razor blade cutter and scratched a line in the backing plate. I scratched from one side to the middle and then from the other side and to the middle so there was no risk of slipping and cutting into the paint. (Well, very little risk anyway. You may wish to find a marking pen that will work.)
Now remove the license plate frame. Then remove the two bolts holding the backing plate to the car. I don't know what kind of tool is supposed to take them out but I found that a 5/32" allen wrench did the trick.
Now you'll find that the backing plate is stuck rather firmly to the car. Don't worry, it's just some double-stick foam tape. Get your fingernails under a lower corner and pull the backing plate away from the car. Apply steady pressure and let the foam tape slowly give. DO NOT just yank it off! Just keep pulling until you've got the corner an inch or so away from the car.
The foam tape should stick to the car in some places and to the backing plate in others and just stretch between the two. Instead of just pulling until it breaks, carefully snip the tape with a pair of scissors wherever it is stretching between the car and the backing plate. The result looks like this:
The tape stretches a bit and you do not want there to be overlap of the tape when you put it back together so cut off a little from the ends of the tape. Resulting in this:
That last one is the stack of little pieces of foam tape that I cut off.
If you've got some of the foam tape for body molding you can just remove all the tape piece and replace it with new. It comes off fairly easily. A lot easier than the stuff holding the badges on. I probably would have done this except I had just used the last of my tape last month when a body molding piece peeled off my Jetta.
Once removed, if not completely removing the foam tape you should protect it from getting any dirt or plastic shavings on it. I used a plastic grocery sack and just stuck it to the tape.
Now your ready to cut. To cut it you can use a dremel tool, jig saw, hack saw, or whatever else you've got around that could work. I even considered a pair of tin snips but was afraid I would crack the plastic. Anyway, since I don't have a dremel tool and my jig saw would require an extension cord, I opted for using a hack saw with a soft-metal blade (larger teeth). The jig saw would have been better but all my extension cords were being used for Christmas lights.
I started the cut about 1/4" above the line scratched on the bottom of the backing plate. I think that should be adequate for any size plate frame. I will be replacing the dealer frame eventually. After cutting, trim the the edges with a razor blade cutter to remove any sharp edges and loose pieces. Here's the result:
Just put the backing plate back in place, attach with two bolts, and attach the license plate and frame. All done! Here's the end result: