Take the place back and remove that rubbish they filled it with.
In some ways they are doing that.
"Due to its long history as both a church and a mosque, a particular challenge arises in the restoration process. The Christian iconographic mosaics are being gradually uncovered. However, in order to do so, important, historic Islamic art must be destroyed. Restorers have attempted to maintain a balance between both Christian and Islamic cultures. In particular much controversy rests upon whether the Islamic calligraphy on the dome of the cathedral should be removed, in order to permit the underlying Pantocrator mosaic of Christ as Master of the World, to be exhibited (assuming the mosaic still exists).
However, work has reportedly been purposely slow on the Hagia Sophia due to its important position and symbolism within the Eastern Orthodox Church. The Ecumenical Patriarch of the Greek Orthodox Church has claimed that the Turkish Government has denied offers to provide monetary assistance for the further restoration of Hagia Sophia in order to downplay its importance. Some Orthodox and Catholic Christians have gone so far as to demand the return of Hagia Sophia to the Orthodox Christian religion as a condition of Turkey's entry into the European Union."
Decent write up on wikipedia regarding it:
http://en.wikipedia.org/wiki/Hagia_Sophia