How do I remove a ceiling speaker cover?
I don't know the speaker brand, but I'm 99.9% sure it's going to be magnetically held. Now that you know that you'll go peel it right off. Be careful you don't bend it, they can be very thin.

How do know the speaker has adjustments?

Continued:

Hum! I was involved in a commercial auditorium theater system installation and the ceiling and cabinet mounted speakers all had flat ribbon magnets on the entire front perimeter of the enclosures. And the very thin, light weight grills snapped to it as tight as could be. I see for the Polks that @Steven have, only the perforated inner grill is friction held for its entire perimeter to the permanently installed outer frame providing a similar firm and continuous attachment. But I would think you'd recall that from when you had the one off. I would also think that some sort of a clip or spring loaded mechanism would be the least desirable method possibly allowing the grill to vibrate and make sounds of its own, but maybe that's it. Try pushing on the grill on each edge and see if there's any movement. I guess the other possibility is that the painter just finished painting the ceiling and put the grills right back up on the wet paint.