In this miracle (Matthew 15:21-28; Mark 7:24-30), Jesus uses His meeting with a pagan woman from beyond the borders of Judea to illustrate the future potential of the Gentiles. While Christ spent most of His time ministering to Israelites (Matthew 15:24), on a few occasions He did mercifully intervene on behalf of Gentiles.
The Gentile identity of the woman who sought exorcism for her daughter is emphasized three times in the accounts: in Matthew 15:22, she is "of Canaan"; and in Mark 7:26, she is called both "a Greek" and "a Syro-Phoenician," a person from Phoenicia, then regarded as part of Syria. Jesus performs this miracle in the coastal area of Tyre and Sidon, the same area where Elijah performed the miracles of providing meal in the barrel and raising the Gentile widow's son from the dead (I Kings 17:8-24).
Later, the apostle Paul stopped at Tyre and met with some Christians there (Acts 21:3-4), showing some of the influence Christ had on these Gentiles. Not only was this miracle part of that influence, but Luke 6:17-20 also tells us that many from that area came to Judea, bringing their sick and demon-possessed to Christ for healing.
Regarding the exorcism of the daughter, we see that Christ declares the girl to be healed, and it is so. Clearly, the woman believes that distance does not matter regarding Christ's power to heal, for when Jesus tells her to go home and that her daughter is healed, she leaves Him with complete confidence that His word is true and omnipotent. She is another of Jesus' "other sheep" (John 10:16), a Gentile, not an Israelite to whom He had primarily come. She undoubtedly made this miracle known to other Gentiles, opening the door for the apostles to proclaim Christ's purpose for coming into the world: to bring salvation one day to all humanity.
Martin G. Collins
The Miracles of Jesus Christ: Exorcising a Syro-Phoenician (Part Two)