I'm sorry but I can't see any horizontal lines from your picture... Nevermind, I just saw your newer pictures... Now I can see the line, but still can't tell what it is...
In any case, here's what to test.
1) Take a screenshot of an image when you see the line the most (according to your post, that would be a darker color).
2) Send that screenshot to your computer. Can you see the line there? If you can (which I'd think it's highly unlikely), it's a software issue, and either a factory reset would fix it or a new unit would.
3) If you can't see the line in the computer screen (which I'm 99% sure you won't), it could be a number of things.
a) Defect in the screen protector. I'd tell you to try to remove it and see if it goes away, but I know that could mean losing a screen protector since most are not re-usable.
b) Defect in the display panel. This is way more difficult to diagnose since that would be the panel under the glass. These defects are usually sharp lines of 'dead' pixels, so it would look like a very sharp, straight line, not a jagged, blurry one.
c) Defect in the display circuit. Similar result to the one above, but the defect would be in the connector making the display show that dead line of pixels. Usually this defect shows 'dancing' or 'twinkling' pixels that don't match the colors or images that you're displaying.
d) A defect in the display driver. Not the connector, but the actual image driver chip. This would produce a similar effect to the above two, but would also show on any external displays you connect your phone to.
e) A defect in the glass itself. This would be a blurry line, usually with a rainbow-like effect if you hit it with a light and it would distort the image in different places if you look at it from different angles (if the defect is always at the same, precise spot no matter how you look at it, it's not the glass).
For both a and d, you could test the output image on a TV using an MHL cable or since this is a Note 4, via SideSync onto a computer or tablet via USB or WiFi. If the image beamed to the other device doesn't show the lines, it's not the software or image drivers.