An article on www.itworld.com shared tips on laptop maintenance, including the use of vinegar and distilled water to clean the screen. The tip is noted below:
If that doesn’t clean the screen, make your own cleaning solution by mixing distilled water (make sure it’s distilled) and white vinegar in equal proportions into a spray bottle. Turn off your laptop. Spray this mixture lightly onto the microfiber cloth, not onto the monitor. Wipe as described above, then wait ten minutes before booting up.