Okay I managed to get it out by really jabbing the screw driver into the side of it (see attached picture - what would you call this part?). So I have two issues now:
1.) I probably need a replacement part for this, also the cap for the lever is missing.
2.) I have no idea how to take this thing apart (was trying to adjustment the max temperature). There's a screw behind the red threaded insert, at the very end, but when I loosen it it gets to the point where it start clicking and not coming out anymore. At that point I have no idea how to take anything apart.
Can anyone identify this valve so I can find the instructions? It's got the Show Home by Moen logo on it but I don't think it's the part I originally thought.