Summary: The woman was rebuffed by Jesus, yet responded with a deep faith in God's love for all people independent of gender or race. The people of the Decapolis were presented with an overwhelming demonstration of Jesus' Messianic power yet without believing.
In the previous section of Mark 7 Jesus is confronted by the Pharisees over the issue of washing hands. He responds by pointing out that their reliance on their traditions has blinded them to the much more central issue of purity of heart.
He points out to them that washing your hands won't make you clean. You first need to be clean on the inside. The Pharisees were too concerned with outward appearances and not enough with inward reality.
Well in today's reading Jesus leaves the region of Galilee and travels to the region of Tyre, over on the Mediterranean Sea in what's now modern Lebanon. Now I don't think he's just going off for a few days at the beach to rest and recuperate as you or I might. Rather he seems to be getting away from the places where the Pharisees can come and speak against him; perhaps even try to kill him.
He goes there incognito, obviously trying to avoid the attention of the locals. Perhaps he wanted to escape all the attention, hoping to have a break from the constant demands for healing that he'd experienced back in Galilee. But when he gets there he encounters someone who reflects exactly what he's just been saying to the Pharisees: a woman who would have been considered unclean by the Jews and yet who shows that on the inside she has a pure heart of faith in Jesus.
Jesus' desire for secrecy is thrown out the window almost immediately. It appears that even in Tyre he was too well known. The stories about him must have been going around the whole countryside and I guess in a small town the word would get around fairly fast that the teacher had just arrived. And so one of the women of the town hears that he's there and she immediately comes to him to ask him to heal her daughter who's possessed by an evil spirit.
Well, what would you do? Here's this woman. She's described as a Gentile, born in Syrian Phoenicia. So she's a pagan. Not even a Jewish proselyte. She's a foreigner, of a race that are ancient enemies of the Jews. And worst of all, she's a woman. No self respecting Jewish man, especially a Jewish rabbi, would speak to a woman without her husband present. So here was a great dilemma for Jesus. What was he going to do? In Matthew's gospel we're told that he simply ignores her at first, until her crying and begging become too much for his disciples who ask him to send her away. Up to this point it seems that the barriers of sex and race and religious tradition are holding him back. But then Matthew tells us what may be the real reason for his hesitation. There Jesus says "I was sent to the lost sheep of Israel."
He seems to be saying that his calling is very clear. He's been called to go to the people of Israel. First he has to minister the gospel to them. It will only be later that the gospel spreads to the ends of the earth. When he later sends out his disciples just before his ascension he tells them to go to Jerusalem and Judea and then to Samaria and the ends of the earth. There's a primacy to the nation of Israel that he isn't yet ready to take away. And so this woman's request is refused in a fairly harsh manner: "Let the children be fed first, for it is not fair to take the children's food and throw it to the dogs."