Default [Q] Does your screen look very smudgy?

I can't really explain what I'm thinking of, I don't have a problem with the LCD itself, but on the surface of the screen it looks really smudgy, but in a weird way. My older phone or tablets screen had fingerprints of course, but it's different on the XL. You can't see it in the dark, but outdoors in the sun (even now in winter) I can barely see the screen because of it. I'm sure you know what I'm talking about if yours also loook like mine.

That's the only reason I use a screen protector, but I don't like the feel of the screen protector so I'd like to remove it.