The international legal document in question says that if a cultural property is "exported" from a country that has come into its possession from the occupation of a territory, then that 'importing' country should seize the property in question. This is what Jordan is asking. The Israeli position on this case, is that the scrolls have not actually been "exported." The Canadian law that came into force to ratify (for Canada) the Hague Protocols also speaks of the "export" of cultural property, but does not actually define the word "export." Canadian courts, however, have, albeit in different contexts. For example in this case, the courts have said that to export generally must have a commercial purpose of some kind, or at least have the intention of an item being permanently sent from one country to another. The case of a museum exhibit loaned from one country to another would therefore not meet the definition of export and so, it would appear that the international and domestic legal provisions relating to cultural goods do not hold up.
A few other points should be made about this latest request. The first one could be termed Jordanian "interest" in the dead sea scrolls. The Dead Sea scrolls are a cultural document that relate to Jewish culture. They include almost the entirety of the old testament and though they were found in territory that Jordan occupied, their link to a distinct Jordanian culture seems dubious. One could make a similar claim about Roman artifacts found in Israel, or in any other part of what was the Roman empire, for example, by suggesting their return to Italy. The presence of these artifacts do not necessarily relate to the culture of the modern state, but may speak to the history of that part of the world. The scrolls do, however, relate directly to Jewish history and the history of the Jewish people. Even if the law were to apply in this case, the results of its application would seem to be an absurd situation: documents, related to the Jewish people would be seized by Canada because another country, whose connection to the scrolls is geographical, questions whether artifacts of Jewish history belong in the custody of a Jewish state.
Moreover, the Jordanian interest in the scrolls seems to be somewhat new. If the scrolls were taken from Jordan in 1967, why has Jordan not been actively pursuing this claim more vocally since then? Jordan may have addressed cultural property when it made peace with Israel in 1994, but did not. Jordan could also have made similar diplomatic requests to the many countries where the scrolls have been exhibited since 1993. This does not seem to be the case either.
One reason for this new interest from Jordan may be the result of Palestinian pressure on Jordan to act. The Palestinian Authority, not being a state, is not a party to the protocol on cultural property the way Jordan is. When the exhibition in Toronto first opened, Palestinians protested that the scrolls had been illegaly taken from "Palestinian territories." They thought the entire exhibition was illegal and should be cancelled. To this claim, the same question can be asked: what is the Palestinian interest in obtaining what is clearly a Jewish document, especially when the Jewish state is and has been a good steward of these precious archaeological documents. The answer may be political.
If the scrolls were returned to Jordan, this would be an admission that at the time they were taken by Israel, Jordan was rightly sovereign over the land that they were taken from. Similarly, if the Palestinian claim that the scrolls should be returned to Palestine is upheld, then there is an acknowledgement that the land from which they were taken is Palestinian, not Israeli. In other words, the argument being made by Palestinians and Jordanians is that the scrolls belong to whoever held the land they were taken from (in this case, east Jerusalem) and so if it is found that the scrolls are Palestinian, then the land must be Palestinian too. The interest may be less about the scrolls and more about the land. Like the land, Jordan and the Palestinian Authority are saying that they don't know to whom it belongs, but they're quite sure that it's not Israel.
Of course, it's not Jordan either. The ironic element in this whole episode is that the last sovereign power over both the area the scrolls were taken from and East Jerusalem (prior to the unrecognized Israeli annexation of East Jerusalem) was probably the Ottoman Empire. When that empire collapsed, the British took over, but their status was as a mandatary--a guardian--not a sovereign. After the British, Jerusalem was to be international and the West Bank, Arab. In 1948 Jordan occupied the West Bank and East Jerusalem in much the same way that Israel does now. So, the scrolls would be...Turkish?
For Canada's part, Foreign Affairs and International trade seems to be indicating that they're staying out of this one, and it seems, may just do nothing.