How to remove black stains on rain jacket caused by backpack?

So I have white north face venture rain jacket that I got around a year ago and most of it is nice and white - except for the bottom part of the back and the end of the sleeves. I wore this jacket to school a lot so of course the end of the sleeves are kinda blackened from resting it against the desks and while writing with a pencil.

However, I also wear a northface backpack and the back of it is cushioned with black mesh. The black mesh is in contact with the bottom part of my back and this considerably blackened the bottom of my rain jacket. I've tried removing the "stains" (more like just blackening from rubbing against my backpack so much) with hydrogen peroxide but it didn't do anything :(

I really really REALLY like this jacket but the blackening of the back and sleeves is extremely obvious and I just want to know how to remove the blackening...

Thank you for any suggestions!