Yes, that's the slight downside associated with the use marble. But there's a method I think to absorb the stain out. A known technique is to apply a 'poultice'.

Kinda of like going to a TCM sinseh or 'teet ta yi' and they prepare a herbal mix that works on the swollen ankle or area in pain after a massage which is not removed until the next day.

But the content of this poultice is meant to remove the stains from marble. Same principle applies to granite and perhaps the content differs slightly. See here.