Mark 7:24-30

"And from there He arose and went away to the region of Tyre. And when He had entered a house, He wanted no one to know of it; yet He could not escape notice. But after hearing of Him, a woman whose little daughter had an unclean spirit, immediately came and fell at His feet. Now the woman was a Gentile, of the Syrophoenician race. And she kept asking Him to cast the demon out of her daughter. And He was saying to her, 'Let the children be satisfied first, for it is not good to take the children's bread and throw it to the dogs.' But she answered and said to Him, 'Yes, Lord, but even the dogs under the table feed on the children's crumbs.' And He said to her, 'Because of this answer go your way; the demon has gone out of your daughter.' And going back to her home, she found the child lying on the bed, the demon having departed." (Mark 7:24-30)


Jesus saw faith in this woman, and made the decision to come to her aide based on her faith in God. Jesus saw the persecution she had suffered because of being a) a Gentile Jew (abhorred by mainstream and very religious Jews), and b) because she was a woman and regarded as inferior to the men. Jesus understood that she was still humble and not angry at the Jewish religion that was persecuting her, and that's how He came to know of this woman.

She was a Gentile - what mainstream and overly religious Jews at the time considered unclean, and were sometimes even referred to as dogs. Though Jesus wasn't calling her a dog, he was only making a reference to the gesture by saying that he had come for the children (Israelites - God's children), and that they would need to be fed before all else. It was a metaphor, not an insult. Jesus was referencing that it would be unwise to give all the good food to the pets before feeding the children. He was also stating that all others would be fed after the children. The Gentile woman showed great humility and diligence in saying that "even the dogs feed at the children's crumbs". Because of this, Jesus told the woman to return home to her daughter, who was now healed. She needed not wait, although she was willing to, and Jesus was pleased with her humble determination.

You're right that this could possibly have been interpreted in a manner that was condescending to the woman. Again, it was making a reference to the term "dogs", which was thrown around lightly by many hardcore Jews of the time. But again, this isn't how Jesus was referring to her. He was often considered the same, and many times far worse, to those same Jews.