A.T. Robertson Commentary Matthew 15:22

"And behold, a Canaanitish woman came out from those borders, and cried, saying, Have mercy on me, O Lord, thou son of David; my daughter is grievously vexed with a demon." — Matthew 15:22 (ASV)

A Canaanitish woman (γυνη Χαναναια). The Phoenicians were descended from the Canaanites, the original inhabitants of Palestine. They were of Semitic race, therefore, though pagan.

Have pity on me (ελεησον με). She made her daughter's case her own, "badly demonized."