To scuff, scratch, dent, or otherwise ruin the smooth surface of something. A noun or pronoun is used before or after "up." You're going to mar up your screen if you carry your phone around in your pocket without a protective cover of some kind. Look at my brand new car! Someone scraped along the side and totally marred it up!
mar something up
to dent or scratch something; to harm the smooth finish of something. Please don't mar the furniture up. Don't mar up my desk.