How do I remove this wall plate with no visible screws?
It's not complicated, you just haven't used one before.
I use ones like it all day long.
The screws are hidden under the little rectangular plastic bits at top and bottom. Typically you push one end in and pry the other one sideways until it pops up. Sometimes you just have to pry one end until it bends far enough to release, but usually it slips under the other end if you push the other end in.
Here's one fresh out of the bag, with one opaque and one clear plastic screw cover (it comes with two of each, the clear ones normally have labels under them, which hides the screw)

OK, the other two pictures I tried to take came out even worse. The two screw covers have a lip that keeps them in place, but they are flexible so that they can bend to allow insertion/ release, and there's extra space so they can be pushed back at the end to slide sideways (on most of them, this is a design cribbed from Ma Bell back when there was only one Ma Bell.)