Instead of India having to prove that the item in question belongs to it, the US will automatically offer it for return once the Cultural Property Agreement (CPA) comes through.
Once the objects reach India, the ASI (which functions under the aegis of the Ministry of Culture) also decides if the object is to be returned to its original place, and handed over to the respective state government, or whether to display them at a museum dedicated to repatriated antiquities at Delhi’s Purana Qila.