Something I like to do is read these Bible stories and put them into our language. It often produces a very different take on the passage. This is a good example.
This woman comes to Jesus begging him to heal her daughter.
Jesus: "I was only sent to Israel."
Woman: "So pretend I'm an Israelite. My daughter needs you!"
Disciples: "Go away. You're bugging him."
Woman: "I'm not talking to you clowns, I'm talking to him."
Jesus: (I see a tiny twinkle in his eye here.) "You don't take good food and feed it to dogs."
Woman: [Cynically] Oh really? Even dogs get to eat the crumbs that fall off the table. How about a few crumbs for my daughter?"
Jesus: [Grinning] "And there it is. Your faith is greater than any of these people who follow me day after day. Your daughter is fine, go see her."
A very different spin on a familiar story. The fact that she persisted in spite of everything tells me she wasn't afraid to get in his face a little, which of course is what he was after. He planned all along to use her as an example to squeeze more faith out of his peeps.