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:
Clean the screen when it needs it. If you can’t see the email for the dirt, it’s time to do a little cleaning. Start with a dry, microfiber cloth–the sort you get at an optometrist’s office (you can also buy them at photo and computer stores). Move it in circular motions. Be gentle, but apply slight pressure on particularly stubborn spots.
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.