NOTE: a pysankar from Europe reports that using the Mr. Clean-type "Magic Eraser" sponges removes these marks quickly, cleanly, and without damaging the cuticle. This appears to be a promising solution to this problem.
Previous answer: There is, generally, no good way to get the date off of an egg without damaging the cuticle (the outer layer of a shell). The egg producers are making them to be eaten, not to be decorated, so do not take this into consideration. The dye must be permanent enough not to come off when the egg sweats (when moisture from the air condenses on its surface) in order to be useful, so it's generally not removable in a simple, non-abrasive way.
Some date stamps are more permanent than others; it is worth trying to wash the stamp off with mild dish detergent (e.g. Ivory) and a Scotch-Brite pad.
Most people who use dated eggs for making pysanky simply leave them on, and either incorporate the colors into their design, or work around the marks.
It's best to avoid eggs with these marks when making pysanky.
The best dye for Easter eggs is just regular food coloring.
It's harder to paint eggs than to just buy some egg dye and dye the eggs a certain color.
Dye them.
Dye them! Or devil them.
Most Easter egg dyes are water based, and so will re-dissolve in water if given the chance. If the egg becomes moist (even if held in a damp hand), the dye will come off. In the case of eggs meant to be eaten, this is not a very big deal. In the case of eggs made to be saved, like pysanky, this can be a problem. That is why most pysanka artists coat their finished eggs with a protective varnish.
Sure, people have been doing it for decades.
Berry Juice
2 weeks with refrigeration.
berry juice
1907
*dye ? as in change her hair colour? Britney spears is not dead!
get some egg dye (any color) and dye 3 not hard boiled eggs.Then microwave the three eggs on a plate.NOTE only one of the three eggs will glow