Dr. Ze’ev Goldmann, founder of Akko Museum, showed me this chancel screen with David's Star and with inscribed Greek cross (upper left) From Khirbet Carmel near Hebron. Photo is from Abel& Barrois, Revue Biblique (RB) 1929 p. 584. There were found three Byzantine Churches in Carmel from the 5th-6th centuries C.E.
Carmel is mentioned in the Bible:
I samuel 25:2
Now there was a man in Maon whose business was in Carmel; and the man was very rich, and he had three thousand sheep and a thousand goats. And it came about while he was shearing his sheep in Carmel