I've done several consults lately for women who are currently breastfeeding their babies. They have asked if breastfeeding and laser tattoo removal are compatible. As an OB physician, my answer is "no".
When you consider the process of the removal of the ink from shattering the ink with the laser and then allowing the body's natural defense cells, the macrophages, to gobble up the particulate and send it through the lymphatic system and then into the blood stream to ultimately be excreted through the kidneys, why would you want to risk the ink particles getting into your breast milk?
No one will ever conduct a study of how much gets into breast milk and if it causes the baby problems because that would be an unethical research project and who would volunteer and potentially put their baby at risk? Pumping and dumping does not even work as it does in the case of medications because once the ink is shattered, the body continually works to dispose of it over the next several weeks. Having practiced obstetrics and being a mother myself, I know breastfeeding moms are a cautious group when it comes to medications and exposure to chemicals. Why take the risk? Wait until you wean your baby, and then come to get your tattoo removed by laser.
Incidentally, the same argument goes for pregnancy. We don't know for sure if that ink is going to get across the placenta to the unborn child. Please err on the side of caution for both pregnancy and breastfeeding.