What does it mean that even the dogs eat the crumbs (Matthew 15:27)?

Response

Matthew 15:27 recounts the reply of a Canaanite woman to Jesus. She stated, “Yes, Lord, yet even the dogs eat the crumbs that fall from their masters’ table” (ESV). The full dialogue is as follows:

After that, Jesus left and went to the region of Tyre and Sidon. A Canaanite woman from that area approached him, crying out, “Have mercy on me, O Lord, Son of David; my daughter is severely tormented by a demon.” However, he did not respond to her. His disciples urged him, “Send her away, for she keeps crying out after us.” He replied, “I was sent only to the lost sheep of the house of Israel.” Nevertheless, she came and knelt before him, saying, “Lord, help me.” In response, he said, “It is not appropriate to take the children’s food and throw it to the dogs.” She replied, “Yes, Lord, yet even the dogs eat the crumbs that fall from their masters’ table.” Then Jesus commended her, “Woman, your faith is great! Let it be done for you as you wish.” And her daughter was immediately healed. (Matthew 15:21-28;ESV)