The preinstalled protector is really just to protect the glass finish during assembly and shipping. It's not ment as a long term protection for daily life usage It really does nothing to protect from bangs or knocks and only really protects the glass finish from scratches. Best thing to do is get a third party screen protector and get rid of the one on there.
Well that's one thing you'll need to look into. There are plenty compatible with the fingerprint sensor. I found out to my cost not to use those long term when an innocuous knock broke a screen on one of my old phones. It is a protector of sorts. But as you are finding out, it gets marked easily