Can you show an image for reference on these pieces that are not supposed to be removed? I think I know what you are referring to but just want confirmation .
It's these large plastic air dams that I've circled in red. They are held on by 3 clips. Very easy to remove and add back without breaking their retaining clips.
Also, on my GTI, behind the AC condenser, I had also had these like "miniature" air dams which I believe served as thin rubberish seals that's go between intercooler and condenser, and those barely fit my new intercooler though--I tried my best to realign them on my new intercooler, using a photograph I took before disassembly of the oem setup as reference. I didn't see these seals mentioned in any of the videos or tutorials I came across.
Lastly, you might have to trim the large plastic air dams a little bit b/c some aftermarket intercoolers are wider than OEM and so the air dams have to be modified. I did not have this issue myself.