OK. Got my answer from a sexy girl voice at SE.  

Pre-applied screen protector.
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About: 
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It is actually called "shatter proof sheet with scratch resistant".
It is not at all a screen protector and it is not 100% unscratchable.

Main Points: 
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1) The main purpose of the pre-applied sheet is to protect the phone LCD from shattering. IE. when u drop your phone, when u accidentally sit on your phone while it being in your back pocket.
Basically the function of it is to ensure the glass does not shatter and fly all over the place or your pockets. It is 1/8" thick and has strong adhesive.

2) It is scratch resistant and not scratch proof. Yes you can still have scratches to it if you take a key and purposely scratch it. But it will protect from light scratches ie. when you put it in your pocket with keys in it.

3)To avoid tiny glass going into the phone if the screen breaks. There is a lot of adhesive on the sheet to stick to the main LCD of the phone to avoid tiny pieces of glasses going in/out of the phone case.
Conversation on Main Questions:  
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me: Should I remove it?
SE girl: (jokingly) If your car has a double layered tempered windscreen which does not shatter on impact. Will you remove it and fit in a single layer windscreen?
me: Nope, it's safety.  
SE girl: there you go. It's the same as our phones. For safety to the customer and the phone internals.
Me: Phone internals?
SE Girl: Yeap, you don't want glass in your phone if they did not clean it well during replacement. You certainly do not want glass falling in your ears too. 
Me: If i do not remove it can i put a screen protector on it?
SE Girl: You can, there will be a slight degrading in display and responsiveness but not too noticeable.
Me: What about matte screens?
SE Girl: Matte screen will in general degrade the display and responsiveness regardless with or without shatter proof sheets. But then again, it would not be too extreme.
Me: What if the Pre-applied screen has too much scratches and I need to replace them? 
SE Girl: You can get SE Shatter Proof Sheets at our SE Service Centers soon. After market Screen protectors with good adhesives can be used too.
Me: Is Zagg a good brand of screen protectors.
SE Girl: I'm sorry, I cannot comment on non SE products.

**** Conversation goes on for some other questions since i like listening to her yummy voice.  

My verdict: I'm not gonna remove the pre-installed sheet period!

Test:
I've put in a Matte Screen protector (Brand:SKOOL) for my phone. I do not like how the screen looks now. The Vibrant color has disappeared completely. Responsiveness of the touch screen has minimal difference.
Plus side... there is no more oily smudges on the screen and much easier for scrolling.

Overall Verdict: Tempted to remove the matte screen protector but will wait till Zagg has released it's screen protector for ARC. Will then try Zagg invisible shield and valuate if that has the same effect to the display. If Yes, I will remove it as well and just use the pre-installed sheet instead.

Note:
You guys make your own choice whether to remove or keep it in. I'm in no way suggesting or trying to influence anyone.
I'm just sharing information.