Beside a nondescript stretch of highway linking Bethlehem to Jerusalem, there’s a large shiny rock and a cluster of olive trees. This place, called Kathisma or “seat” in Greek, is said to be where the Virgin Mary rested and drank from a well, not long before giving birth in a stable to Jesus.

The only clue to that history is the ruins of a Byzantine church, with a vibrant mosaic floor peeking through mud and smashed beer bottles. And while the ruins themselves remain in the hands of the Greek Orthodox Church, all the surrounding East Jerusalem property has been leased by the church to an Israeli company, according to municipal records.

The Greek Orthodox Church, which serves as a custodian for many such Christian sites in Israel and the Palestinian territories, is coming under increasing criticism from its followers for repeatedly giving up control of its property through land sales or ­multi-decade leases.

The church’s practice of selling and leasing its properties has caused a split between its followers, who are overwhelmingly ­Arabic-speaking Palestinians, and the leadership, or Holy Synod, made up mostly of Greeks.

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