The ITNJ exists outside and above the jurisdiction of any one nation or country by the authority of the People of the World.
The sovereign People of the World are the source of authority. If the People weren’t sovereign, they would not be able to authorize a sovereign government, because you cannot delegate authorities you do not have. The People of any nation or country or territory have the right to delegate their authority to representatives they choose to run their government. Case in point: the government of the United States of America is allegedly founded and maintained by the consent of the governed.
Just as the People can authorize their governments to act on their behalf, the People can authorize their Tribunal, the ITNJ, to act on their behalf, and delegate their sovereign authority to administer Natural Law. By their signatures ratifying the Treaty of the International Tribunal for Natural Justice, the People of the World mandate the establishment of the ITNJ and delegate to the officers of the ITNJ their authority to administer Natural Law for all the People of the World, in all the territory of the World.