Citations: Matthew 15:21-28 || Mark 7:24-30, Matthew calls her a "Canaanite"; Mark, "a Greek, a Syrophoenician by race." A healing/exorcism worked at a distance, on Gentile soil.
Narrative
Jesus withdraws to the region of Tyre and Sidon (Gentile territory) and wants no one to know. A local woman whose daughter is severely demon-oppressed comes crying, "Have mercy on me, Lord, you son of David! My daughter is severely possessed" At first Jesus answers nothing. The disciples urge, "Send her away, for she keeps crying out after us." Jesus: "I was not sent but unto the lost sheep of the house of Israel."
She kneels: "Lord, help me." Jesus: "It is not right to take the children’s bread and toss it to the dogs." She answers, "Yes, Lord, but even the dogs eat the crumbs which fall from their masters’ table." Jesus: "Woman, great is your faith! Be it done to you even as you desire." Her daughter is healed from that hour, Mark notes she returns home to find the child lying on the bed, the demon gone.
The hard saying, "the children’s bread and throw it to the dogs"
This is one of the most discussed exchanges in the Gospels, and the major readings are set out here without choosing one:
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A drawing-out of faith. Jesus tests and then publicly honors a faith he means to reward; the diminutive he uses (kynaria, "little dogs / household pets," not street curs) and the whole framing invite her famous reply. The silence and the saying are the setup for "great is your faith." -
The salvation-history priority voiced. Jesus states the real order of his mission, "to the Jew first" (cf. Romans 1:16; Matthew 10:5-6), which the woman's faith does not overturn but leaps ahead of: she asks only for the crumbs that already fall while the children eat. A foretaste of the Gentile mission that the cross will open. -
A genuine-encounter reading (minority). Some read Jesus as truly moved and his stated mission as enlarged in the moment by her faith. The view is recorded here; most interpreters hold one of the first two.
Theological significance
Gentile faith commended. With the [centurion], this woman is one of only two people whose faith Jesus calls "great", and both are Gentiles. Their stories bracket the ministry as signs that the gospel will cross every boundary.
Persistence and humility. She accepts the lowly image and turns it into an argument for grace rather than against it, wit born of desperate trust. She does not demand a place at the table; she claims the crumbs, and receives a full answer.
Deliverance at a distance. As with the official's son and the centurion's servant, Jesus heals without going or touching, his word reaches across the miles.