Isopropyl alcohol on a Q-tip or Kleenex and gently applied with light pressure will get rid of the mark with a few tries. You need to check that alcohol will not cloud the screen however. Most LCD screens can be cleaned with 50/50 alcohol with no problems. The key is NOT to use much pressure or you can damage the screen in short order. Be sure to put the cleaning solvent material on a cloth or Q-tip, never directly on the screen.
Goo Gone is great stuff and will work remove Sharpie maker better than alcohol, but bear in mind it is mainly a citris oil solution and could be difficult to entirely clear off the screen. I have not idea what it could do the notebook screen material but it is harmless to most plastics but will dissolves gums and goos.
