Ministry to the Gentiles

Jesus came for "the lost sheep of the house of Israel." (Mat 15:23), but what happened when a gentile woman came to Him in faith asking that He heal her daughter? What followed at first may seem confusing but later shows the hope that we can have because of Jesus. Finally, how should this passage from Matthew 15:21-39 instruct our lives and the way we think about others coming to faith in Jesus?