In the first few days of owning this phone, something didn't look quite right around the perimeter of the lens.
It looked like there might have been a piece of protective coating/sticker on its ring, but it didn't really peal off with ease.
I was afraid if I picked at it too much, I was going to damage it. Still, it continued to bug me, and the surface looked a little cloudy and scratched.
Finally, I removed the battery cover and chipped away at it with my fingernail. It is indeed protective plastic, and it is indeed intended to come off.
Yes, it does improve picture quality, particularly for close up shots. The area in which it covers is the light sensor, and having it covered up impacts its ability to function properly.
If you own an S4, take a close look at yours and peel it away if it's still on there. A piece of tape can assist in getting it off.
Just a little tip to remember. The camera takes superb pictures!