Some pictures.That drove me nuts as well. I went to Home Depot and bought some 7/8" rubber bumpers. They slid right of the nuts on the bottom of my plate frame. $1.95 . The bottom sticks out a little more than I like. But, I'll take that over the rattle any day.
Mine came with a couple of foam pads on the surface of the car behind the license plate area to prevent rattling (USA Latitude). When I installed the plate into the frame, there was a rattle between the plate and the frame, but a couple of blobs of Blu-Tack solved that one.
My North came with rubber stops. I then put velcro tape on them and the license plate to stop any noise
NJ plates are no longer embossed and are shaped like pringles chips.I have something similar but it doesn't lay flat. Does yours?