I'm not a medic and have never worked with water purification. I am an RN with a BSN and considerable clinical curiosity.
I'm wondering if the questioner was intending to source iodine as a causative agent in precipitating menstruation, or if the questioner was trying to determine if iodine was an effective agent in removing EDC's from water.
The EPA did a study
http://www.epa.gov/ppcp/projects/evaluation.html on water purification methods and their efficacy at removing EDCs (endocrine disruptive chemicals). EDC's could have an effect on menarche in females. There are steroids from agricultural use that find their way into the water as well as medication waste but this is generally in urban areas.
Bottom line, I don't believe iodine is an effective filter for EDCs if that is the questioner's "question". A healthy body is basically very good at maintaining a steady level of iodine despite excessive or limited intake. I don't see it as a trigger for hormonal imbalance unless the subject already has a problem.
Just my observations, YMMV.