Albert Barnes Commentary Mark 7:26

"Now the woman was a Greek, a Syrophoenician by race. And she besought him that he would cast forth the demon out of her daughter." — Mark 7:26 (ASV)

A Greek. The Jews called all persons Greeks who were not of their nation. Compare Romans 1:14. The whole world was considered as divided into Jews and Greeks. Though she might not have been strictly a Greek, yet she came under this general appellation.