From the book "Très Riches Heures du Duc de Berry" – French (15th century)
This is a Gospel story told in Matthew, Mark and Luke. It is somewhat unsettling as Jesus response to a request to a woman was at best harsh and worst a racial slur. It is unique in that it’s the only time in the Bible that Jesus changes his mind over his response. This story appears in Mark sandwiched between the Feeding of the 5,000 (Jewish people) and the Feeding of the 4,000 (Gentiles).
Jesus had moved to Tyre and wanted to remain unrecognized. He was undoubtedly tired and needed a rest. The last thing he needed was a diversion. However, a woman who was not a Jew approached him, "bowed down at his feet" and said her daughter was tormented by a demon. This could be any number of illnesses. In the Matthew version the disciples advocated sending her away.
Jesus told this Gentile woman that he was only sent to the lost sheep of Israel and that it wasn’t’ right take children’s food and feed it to the dogs.
The woman responded that even the dogs under the table will eat the children’s crumbs. Basically she said "give them to me!" Jesus was moved by her faith and love and healed her daughter.
Many writers focus on Jesus. Did he call her a dog ? Is a better translation "puppy" ? Did he stage this as a scene to show the disciples a better way to treat foreigners ? Was he just having a bad day which he later corrected ? Is this story a transition where Jesus’ mission is enlarged from just a Jewish perspective to a Gentile?
The real focus should be on the woman. She risked making a fool out of herself and insisted on help. The upshot is an example of evangelism – she left paganism and idolatry and followed God. This becomes the setting for the Feeding of the 4,000 gentiles.