Ok, so you've purchased a new toy, one of your kids has claimed it to play with and got greasy(?) finger marks all over it... what do you do?
1) Give your kid an ear-bashing!
2) I can recommend using alcohol wipes (such as specs wipes) to clean the unit all over. Don't use any abrasive / solvent cleaners as they will wreck your toy in no time, especially if used on the screen.
3) If you have not removed the original screen protector from the unit, all the better. If you do have to remove it, try and replace it with another of a similar type. Forum members have suggested recently that Poundland sell iPad screen protectors that can be cut to size. Remember to keep the old protector to use as a template to cut out the new one.