crank the press round till the head lays are in the fully "up" position, effectively where they are when a sheet layed and positioned to be taken by the swing arm grippers, and clean the head lay and swing arm grippers with a strong cleaner or IPA on a rag wrapped round a steel ruler... they probably have oil and old ink built up on them that can scratch...
Otherwise look at smoother positioning, run them harder on edge of sheet or in a gutter if possible, as the lays swing up and away they will help hold the sheet down tighter and hopefully away from the swing arm grippers and minimise scratching...