The Jewish community in Iraq dates back to the Babylonian exile. While many Jews returned to their country, as outlined in the book of Nehemiah in the Old Testament, some remained in Babylon. In fact, the Babylonian Talmud is considered authoritative among Jews to this day. The antiquity of the items found would be extremely interesting to Biblical scholars. There is the Center for the Study of New Testament manuscripts in Plano, Texas, that I am sure would be interested in what might be found there.
There are Jews living in Iran today.
Acts 2.5-10 in the New Testament says that Jews from every nation were in Jerusalem at the time of Pentecost and mentions Parthians, Medes, Elamites and residents of Mesopotamia among them. Parthia, Media and Elam are in what is now Iran while Mesopotamia mostly corresponds to modern Iraq.