That's the oleophobic coating wearing off. Same thing happened to me on my 6s and my Galaxy S5 before it. On my S5, I simply covered it up with a tempered glass screen protector, but I have no intention of using a screen protector on my 6s so it was driving me crazy. I went to the Apple store and showed it to them and explained to them what it was. They said it fell under cosmetic damage that didn't impact the practical use of the phone in any way, but they still offered my a one time screen replacement under warranty. My new screen is pristine (for now) from a smudge point of view, but it has a small portion near the top where the backlight is uneven so there's a darker area between the clock and the battery meter. That's probably an even worse issue, to be honest, but I'm gonna live with it since it's really only visible when I tilt the screen away from me. It isn't apparent when viewed dead on, and I don't want to be *that guy* who goes back to the store and has his screen replaced 5 times for tiny issues. I really hate the inconsistency of these iPhone screens though.