Are Green Card holders working for supranational organizations outside the U.S. required to pay U.S. income taxes?
In general U.S. citizens and GC holders are required to pay U.S. federal income tax whether or not they actually live in the US. This is the position taken by the UN.
However, the IRS’s website states that there are two organizations in the world that are exempt from this rule: the IMF and the World Bank.
Your work for an international organization and the international organization agreement creating the international organization provides that alien employees are exempt from U.S. income tax. Two international organizations that have such a provision are the International Monetary Fund (IMF) and the International Bank for Reconstruction and Development (World Bank).