So, more than two years later I have not removed the screen protector.
The screen quality has gotten better thanks to new graphic driver updates, better optimization for google chrome and windows too (can you believe it that this display has a resolution that was not fully supported years ago?)
Obviously, due to the protector's matte nature, the whites are still a little grainy and more dull than normal. However, blacks are even blacker and darker colours intenser as well. Though it is less accurate than a Vaio Pro screen without a matte protector, the joy to be able to use it in all lighting conditions without annoying glare outweighs that loss of accuracy for me.
As another plus, it makes the laptop look sleeker overall, more stealthy. =)