Need help in removing granddaughter's pencil marks from my LCD computer monitor

First, jam the pencil into her eye (just kidding).
I would recommend a cleaner from Kensington (little spray bottle) and a 3M electronics microfiber cloth.

And then keep pencils out of the reach of the granddaughter.

The pencil probably scratched the screen so after you remove it there may still be marks.
Dont press down hard when cleaning the screen or you will damage it even more. Any basic lens of screen cleaner should do the trick. DONT USE WINDEX!

You could try the scratch remover they use on car paint which basically disolves a very thin top layer to even out the surface. I havent tried this on plastic so you may want to test it on some of your kid's toys before you use it on the screen.

Thanks for the help. cleaned up good using diluted shower body wash.

she must have a gentle touch, you lucky dog.