My guess would be that it's an effect of grease from your thumb/finger and that that is the area of your screen you touch most often. Just a guess though, beyond that I personally would have no idea.
Looks like the oleophobic layer off the screen protector rubbed off in the area you touch the most.
Do you think I should replace the screen protector ?
If you have an extra laying around I don't see why not. Should help you see if it's the screen protector or the glass itself. If it's the glass, you can probably get it replaced at an Apple Store.