Most things natural are not very effective at chelating iron at the level needed for those with iron overload from transfusion. There's just too much of it.
What green tea, as well as all other drinks with tannins in them, will do is to reduce the absorption of iron from the foods you eat when consumed together. So for those who consume large quantities of tea can become low in iron which can result in anemia.
In all my research, I've never come across articles on green tea suppressing bone marrow. That doesn't mean it doesn't exist though. I mostly find that it's protective of the cells and can suppress the bad ones.
Marlene, wife to John DX w/SAA April 2002, Stable partial remission; Treated with High Dose Cytoxan, Johns Hopkins, June 2002. Final phlebotomy 11/2016. As of January 2017, FE is 233, HGB 11.7, WBC 5.1/ANC 4.0, Plts 146K.