Talk to Gynecologist on Glutatathione While Breastfeeding

Can some doctor guide me plz. I am breastfeeding my baby. She is on bf and formula both. I want to ask if I take glutathione supplements then is it going to the baby too theough breast milk? Can I start now or I should wait until I stop breastfeeding completely?? My melanin has increased drastically during pregnancies and from a fair girl I have become v dark now. Thats the reason I want to go for glutathione . My concern is my baby , if it is fine or I should not take these supplements. Thanks