Tweeter Grille Rattle

I've noticed a quiet rattle that's been driving me nuts on the highway and driving around the streets. It seemed to be coming from the passenger side so I did some investigation and I shook the passenger door when it was open and I heard the rattle. I poked my ear around and found it was coming from the tweeter. I pushed on the tweeter grille and the sound went away. To me it sounds like the grille is sticking against the door panel or the speaker causing the noise. I'd like to fix this without taking the door panel off, but it looks like the bezel should come off. Anyone know if the bezel actually does come off? Or do I have to take the whole panel off? I'd like to put a small shim or something in there so it doesn't move anymore.

 

BUMP. My driver side just started doing this. Ever find a quick fix? I really don't want to take off the whole door panel for this.