A lot of computer screens still use plastic, which is something you would not want to sand or try buffing because it's very soft. More and more computers and devices now use have glass protective covers. The LCD screen is beneath the glass on a phone, laptop or iPad. Generally speaking that glass is going to be something called gorilla glass which is made by Corning. This glass is very tough, which makes it harder to scratch but if it does get scratched, it's also harder to fix.
Leo doesn't think a Windshield repair place would work out because they just fill cracks with a resin which would keep a windshield from cracking further, but would it's not invisible. It probably would end up looking like a "blob" in that area of the screen.