How much does the "Ottomans's consent" argument of the British Museum hold regarding the Elgin Marbles?

International law is, as usual, muddled.

• Article 11 of the 1970 UNESCO convention makes the transfer of cultural artefacts by an occupying power illicit. But were the Ottomans an occupying power in the sense of the convention, or a multi-ethnic empire?
  The Marbles had been created by Athens at a time when there was no such thing as a sovereign Greek state. The Athenians would have rejected the notion of such a state unless it meant that they could dominate the other Greek cities. Sparta disagreed and they fought bitter wars. Athens subsequently became part of Macedonia (Hellenic League), and then Rome, and then East Rome (Byzantium), and then the Ottomans. Plus a few more in between. Without hindsight, it is difficult to call the Ottomans less legitimate than, say, Alexander the Great.
• Article 7(a) of the UNESCO convention, banning certain transfers, does not apply retroactively.
• There is the concept of odious debt in international law, which says that debts of a despotic government does not bind a successor state. Attempts to apply this tend to be hotly argued, and the Ottomans were widely accepted as a government at the time, no more despotic than most others.
• There is an ongoing debate, and possibly an ongoing change to customary international law, regarding looted art from colonies. Yet the Ottomans would have rejected any suggestion that they were a colony and not a sovereign empire.

Greece does argue it has a moral claim to the Marbles. So it becomes less a question of international law, and more one of persuasion.

In terms of diplomatic and legal steps undertaken, the Greek government requested the return of the marbles from the UK in 1983, and listed the dispute with UNESCO in 1984.

Since 1978, the UNESCO has an Advisory Commitee to help with the resolution of conflicts, the Intergovernmental Committee for Promoting the Return of Cultural Property to its Countries of Origin or its Restitution in case of Illicit Appropriation (ICPRCP). In 2005, its mandate was amended to include a "mediation and conciliation" process that disputing parties may enter voluntarily. Since then, the Article 4, items 1 and 2 read as follows:

Article 4

The Committee shall be responsible for:

1. seeking ways and means of facilitating bilateral negotiations for the restitution or return of cultural property to its countries of origin when they are undertaken according to the conditions defined in Article 9. In this connection, the Committee may also submit proposals with a view to mediation or conciliation to the Member States concerned, being understood that mediation implies the intervention of an outside party to bring the concerned parties to a dispute together and assist them in reaching a solution, while under conciliation, the concerned parties agree to submit their dispute to a constituted organ for investigation and efforts to effect a settlement. For the exercise of the mediations and conciliation functions, the Committee may establish appropriate rules of procedure.
2. promoting multilateral and bilateral co-operation with a view to the restitution and return of cultural property to its countries of origin;
3. (...)

The committee has no power to force its decisions on anyone, and the proposal of this new mechanism by the secretariat included a clear message that taking part in the mechanism needs the acceptance of both parties:

Mediation implies the intervention of an outside party to bring the concerned parties to a dispute together and assist them in reaching a solution, while under conciliation, the concerned parties agree to submit their dispute to a constituted organ for investigation and efforts to effect a settlement. In either case, the parties to the dispute must agree to participate in the mediation or conciliation exercise. Contrary to arbitration and judicial ruling, conciliation and mediation are not binding and not judicial means of dispute settlement. Terms of settlement recommended by the third party are not obligatory for the States concerned, as they may reject it and have recourse to other dispute settlement mechanisms in the spirit of Articles 2 (3) and 33 of the United Nations Charter.

In 2013, the Greek government requested that the case of the Elgin Marbles should be submitted to this mediation and conciliation process. The UK government and the British Museum declined to take part. The ICPRCP is clearly not happy about this refusal. In 2021, it adopted the following decision:

DECISION 22.COM 6

The Committee,

1. Recalling Article 4, paragraphs 1 and 2 of its Statutes,
2. Noting that the request for the Return of the Parthenon Sculptures is inscribed in its Agenda since 1984,
3. Recalling its 16 Recommendations on the matter,
4. Recalling further that the Parthenon is an emblematic monument of outstanding universal value inscribed on the World Heritage List,
5. Aware of the legitimate and rightful demand of Greece,
6. Acknowledging that Greece requested the United Kingdom in 2013 to enter into mediation in accordance to the UNESCO Rules of Procedure for Mediation and Conciliation,
7. Recognizing that the case has an intergovernmental character and, therefore, the obligation to return the Parthenon Sculptures lies squarely on the United Kingdom Government,
8. Expresses its deep concern that the issue still remains pending;
9. Expresses, further, its disappointment that its respective recommendations have not been observed by the United Kingdom;
10. Expresses its strong conviction that States involved with return or restitution cases brought before the ICPRCP should make use of the UNESCO Mediation and Conciliation Procedures with a view to their resolution;
11. Calls on the United Kingdom to reconsider its standand proceed to a bona fide dialogue with Greece on the matter.

Opinion: This decision has a few strange wordings. Remembering that the committee has no mandate to decide any dispute, it seems to me that no. 5, the "legitimate and rightful demand of Greece" should mean that Greece had a right to ask for the mediation, but is not an opinion that Greece has a right to the marbles. And for no 7, the "obligation to return the Parthenon Sculptures lies squarely on the United Kingdom Government" should be understood as declaring the Government, not the British Museum, to be a party to the conflict, but not stating an obligation to return the Marbles before the mediation and conciliation process has taken place.

But on the face of it, these two points can be easily read the other way.

No other formal steps have been taken. There were more informal discussions between the governments and the museums concerned, but no court has been called, and the ICPRCP mediation process has not been started.