What does Mark 7:26 mean?

As Jesus tries to rest in a home in the Gentile region of Tyre, a Canaanite woman enters the house seeking healing for her daughter. Canaanites were the original inhabitants of the Promised Land. They lived on the shore of the Mediterranean from Lebanon to nearly Egypt, and east to the Jordan River. Descended from Noah's grandson Canaan (Genesis 9:18–25), the Canaanites were known for being wicked and idolatrous. But this woman recognizes Jesus as the Son of David, Messiah of the Jews (Matthew 15:22).

Some versions say the woman is Greek. The woman is Hellenistic and speaks Greek, but ethnically she is a Canaanite and geographically she is Syrophoenician. Syrophoenicia is a portmanteau of "Syria," the Roman province which administers the republic of Tyre, and "Phoenicia," the Greek term for the region known for its purple dye. Syrophoenicia stands in contrast to Libophoenicia which belongs to Carthage in North Africa.

Mark states that the woman begs; Matthew adds specifics. As Jesus seemingly ignores her plea, the woman continues to the point that the disciples ask Jesus to make her leave (Matthew 15:23). Like with the woman with an issue of blood (Mark 5:25–34) and blind Bartimaeus (Mark 10:46–52), Jesus doesn't act until everyone's attention is where He wants it. This is part of the reason for His denial: a deliberate tactic to bring out an important point. We don't know why this woman is so desperate, but considering another demon tried to throw a young boy in fire and water (Mark 9:17–27), her determination is understandable.