In my experience they are usually attached with screws so you can remove them for servicing of the mechanism. It is possible that it could be just friction or small finish nails but if not prying it will break it.
In the third photo i can see what appears to be screw threads in a hole.
The heads of the screws that hold the wood cover in place have ...
Use a thin prybar, carefully.
Look closely at the joints on the bottom trim piece that's in your way, and you'll note that it's not "locked in" to the rest of the frame - because that piece was installed after the crank hardware was. Pry it out of there, replace the hardware, and tack it back in when done.