Matthew 15:23

‘But he answered her not a word. And his disciples came and begged him, saying, “Send her away, for she continually calls after us.” '

Jesus did not answer her. We should note in this regard that she was not addressing Him face to face but calling from a distance, so that there was nothing impolite about it. No doubt in fact Jesus often heard people calling things out from a distance, and could not respond to all who did so. But there was another time when Jesus did not answer, and that was in the case of the woman taken in adultery (John 8:6). It suggests therefore deep thought in the face of a dilemma. He was not quite sure what to do, for the reason shortly to be given, and was no doubt praying to His Father for guidance. Meanwhile she continued to call after them, and the disciples seemingly saw no reason why He should not do as she asked and send her away. Indeed they were clearly getting very embarrassed. They were in foreign parts and she was drawing too much attention to them.