How to remove Atwood Hydro Flame wall thermostat cover?

They usually snap off, but you gotta be careful not to break them. Try gently prying the edges with something thin, like a plastic tool or even a butter knife, starting at the bottom or sides. There might be little clips holding it, so take it slow and work your way around. If it’s really stuck, check for hidden screws or tabs. Just go easy, forcing it could crack the cover.

I imagine it would be fairly easy to add a remote switch. There is already 12v at the switch, you're only missing a ground. 

Interesting, I noticed your anticipator switch is set to zero just like mine. I guess I will keep this setting, seems like its factory setting. 

I have one of those. It's definitely just a pull straight out to get it off. Just hook your fingers in the top by the on/off switch and pull. It's held on on the four side corners just above and below the air vents on the sides.