Glutathione supplements don't interact with your menstrual cycle, so taking it during your period is safe and won't interrupt your flow. It's an antioxidant, not a hormonal product, so it has no effect on bleeding or cycle length.
Next Steps
You can continue your usual dose as per the label instructions, same as any other day.
Health Tips
If you notice unusual bleeding, nausea or any new symptoms after starting it, stop and check with your gynaecologist.