All that wire mesh in the cage probably blocks off 25-30% of the free area. Just like a dirty air filter or a spark arrester adds pressure drop to the system and causes a decrease in power. Removing the screen removes that additional pressure drop through the intake side of your motor allowing more air in. More air means a leaner fuel/air mixture which doesn’t necessarily mean more power instantly, but it does make it possible to gain more power if you can deliver more fuel to the motor to provide the ideal ratio (remapping).
I should have stated that in my case I have a 2008 which came mapped overly rich stock, so just removing the wire mesh helped lean the bike out and create a noticeable power increase.
What I wasn’t sure about was whether or not the TwinAir Backfire filters were really needed once the screen was removed or not, but I thought better safe than sorry.