No one wants a dirty case! Let's get that thing spick and span.
We would suggest using a damp eyeglass quality cleaning cloth first. If that doesn’t remove all the dirt and/or fingerprints, then please remove the case and wash it with mild dish soap and water, then air dry thoroughly. If those options do not work, then try a Mr. Clean® Magic Eraser®. For dry ink marks, you may want to try an eraser from a mechanical pencil and then gently rub it with a dampened eyeglasses cloth.
Do not use cleaners or solvents!