I would think in theory there must be some undamaged layer of paint they could expose?
http://en.wikipedia.org/wiki/Ecce_Homo_%28El%C3%ADas_Garc%C3%ADa_Mart%C3%ADnez%29
As it's become a tourist draw now, do they really want to restore it?
JEDIT:And Kilroy beat me to it. ;)