It would be unthinkable that Jesus would potentially defile himself by associating with a woman like this. However, we cannot forget that Jesus just taught against the concept of clean and unclean, and now Mark is telling a story of Jesus that shows he meant it. A woman comes to Jesus asking him to heal her daughter. But this woman is a Gentile. The intended readers of Mark’s gospel would have been quite interested in this exchange, as they were a largely Gentile audience.
Jesus’ response to the woman is curious to say the least. He does not immediately tell her he will heal. On the contrary Jesus appears to insult her, and shows little interest in her needs. Yet this woman’s brilliant reply, and deep faith cause Jesus to provide healing for her. All she needed after all was a crumb or two for healing.