From the Wikipedia: Vefa Kilise Mosque (Turkish: Vefa Kilise Camii, meaning "the church mosque of Vefa", to distinguish it from the other kilise camiler of Istanbul: also known as Molla Gürani Camii after the name of his founder) is a former Eastern Orthodox church converted into a mosque by the Ottomans. The church was possibly dedicated to Hagios Theodoros (St. Theodore,in Greek: Ἁγίος Θεοδόρος τά Καρβουνάρια), but this dedication is far from certain. The complex represents one of the most important examples of Comnenian and Palaiologan architecture of Constantinople.

In a few pictures you see the 2015 conditions: the area looked almost bombed. I understood from people living nearby that the neighbourhood was being torn down, after which "new old houses" would be built. I saw an example: the by now usual wooden building with possibly inside a concrete structure (the people told me here only wood would be used, I could not check).

I think the idea is that the formerly poorish neighbourhood was a blot on the landscape. Tourists visiting the nearby Süleymaniye mosque would not enter there. But if instead they see all those fine new old houses, they will gladly enter. So restaurants will crop up, hotels, the works. A tourist-geared gentrification. I know this is what happens in every city everywhere all the time, but the scale annoys me.
In the 2015 destruction people live and work. Garbage is being collected and recycled, and I had the strong feeling in several houses that looked gutted large families of - probably - fugitives were living.
The mosque will probably have to wait for some years before it will be “upgraded”. I hope it will keep some of its old feel, Turkish restorers tend to put ancient buildings straight into the 22nd century.