Its safe to assume that when you are teleported to Gantz your body is remade so aliments are taken care of but you raise a good point in saying why isnt the older psychic cured.
The only explainations that i can come up with is that they are, and he just doesnt know it, or when gantz "faxes" you he just remakes a body. Gantz could probably easily see how to fix simple things like cancer or slit wrists (he makes its sound so easy), but something more complexed, or out of his understanding like ESP damage he might not be able to repair.
And shouldnt ESP be Psionics? Cause I mean, Psionics are powers of the mind and ESP is "Extra Special Powers."
um, i dont carve blood......really