That steel wire mesh on the air filter cage is an anti-backfire screen.
In the off-chance your bike backfires through the throttle body, that mesh knocks down the flame so your air filter won't catch fire.
All 4-stroke bikes come with this.
Some guys cut it out (usually on off-road bikes), but I'd leave it there.
If you really want to eliminate it, No Toil makes a Hi-Flow air filter kit that comes with a new air filter and plastic cage without a screen.
The catch is that the new foam filter is treated with flameproof stuff.
The thing that doesn't thrill me about No Toil is the oil - it comes off too easily in my opinion, just as you'd expect with an oil that cleans with plain ol' soap and water, which is their whole marketing angle:
Never mind whether or not it's a better oil for stopping dirt.
It's the cleans-up-easily-because-we-know-you-hate-to-service-your-air-filter pitch they're going with.
Very similar to the chain wax chain lubes when they came out 20 years ago:
Doesn't matter if they're as good as the older chain lubes at actually lubricating anything because when you use too much of it and it flings off onto your rear wheel, you can't see it!!! :)
That was the basis of their original sales pitch.
For air filter oil, I will always use a good, ol'-fashioned petrolium oil, and my choice has always been Maxima FFT.
Goes on watery-thin, and then becomes mega-sticky.
You need a petrolium-based solvent to clean it off, just like God intended it to be. ;)
I've used both the stock air filter and a Twin Air filter.
No performance difference, although the Twin Air filter fit the metal cage a bit more snugly and securely.
Either one works.