Hello everybody,
I removed all that material about a year ago in my 1996 318ti because it was falling apart... after removing it, nothing happened or changed.
That material basically covers all the inside walls of the air filter box, but it seems not to do anything at all...
If that material is breaking apart, do your car a favor and get rid of it before it ends up inside the engine.
I hope this helps
Note: The material is held inside the box by a plastic frame that can be detached from the air filter box, just be careful.