The grey area is just a lighter version of your background, so you can read the conversation easily.
If you remove it, the text will then be on a dark background. Think about if someone uses black text, you won't be able to read it. So the lighter area is a good thing really.
The only way to remove it I presume would be messing with the internals of Messenger. Neither
Mess Patch or
A-Patch have a feature to remove the light area. Sorry.