What an odd thing that initially Jesus ignores the Cannanite woman.
They had hardly arrived when a Canaanite woman came down from the hills and pleaded, "Mercy, Master, Son of David! My daughter is cruelly afflicted by an evil spirit." Jesus ignored her. The disciples came and complained, "Now she's bothering us. Would you please take care of her? She's driving us crazy."
Jesus refused, telling them, "I've got my hands full dealing with the lost sheep of Israel." -Matthew 15:22-24
BBC interprets the scene this way:
"Speaking to Jesus, she addressed Him as the Lord, the Son of David, a title which the Jews used in speaking of the Messiah. Although Jesus was the Son of David, a Gentile had no right to approach Him on that basis. That is why He did not answer her at first."
15:23 His disciples came and urged Him to send her away; to them she was a nuisance. To Him she was a welcome example of faith and a vessel in whom His grace would shine. But first He must prove and educate her faith!
"This Gentile woman’s faith contrasted with Israel’s leaders who were rejecting Jesus." -BKC
I like this angle---that the simple faith of this woman clearly outside the fold--contrasts with the critical spirit of the leaders of the Jews.