I think BS were looking for a cheap, quick, easy fix when they glued the foam to the inside of the mesh. The first GTRs off the line had two separate filters fitted between the airbox and the carb covers as Colin's suggestion above. However, the element was some form of metal wool which often broke up and got sucked into the engine.
This together with failing crank cheek seals (came loose and broke up), generated a significant number of wrecked engines and warranty claims. They had to do something and quick, it was costing them a lot of money. Below is the only picture I've ever found of the original filters.
Personally, I would never dream of running a GTR engine without filter foam fitted to the outside of the airbox as Z's solutions above. Those chrome bores need all the help they can get by keeping the dust out. There is an early post on the site from RC, concerning the importance of properly sealing the air intake system to extend engine life. Will put up a link when I find it. The addition, by the Japanese manufacturers, of effective air intake filtration to bike engines is one of the reasons for the improved reliability and durability they achieved.
Brian