Lord Jesus was indeed sent to the house of Israel or the Jews and not to the Gentiles. But He did not neglect the Gentiles and still took care of the needs of Gentile woman who came to Him. This shows that Lord Jesus Messiah loves the Gentiles despite of His mission to the Jews. As He loved the Gentiles, He appointed Prophet Paul to be an apostle to the Gentiles and the Jews.
Mat 15:24 But He (Jesus) answered and said, I am not sent except to the lost sheep of the house of Israel.
Mat 15:25 Then she came and worshiped Him, saying, Lord, help me!
Mat 15:26 But He answered and said, It is not good to take the children's bread and to throw it to dogs (Greek word "kunarion" means puppy or dog).
Lord Jesus did not mean the woman was a puppy; it was the woman's daughter who was demonized and needed help from Him. As Lord Jesus' mission was sent to the Jews in Israel, He have to do will of His Father. The point to be noted is why Jesus did not reject her worship as God? Without faith in God it is impossible to please Him. But the Gentile woman had such unwavered faith in Lord Jesus and she got what she wanted from Lord Jesus. The moral of the lesson is not Lord Jesus looked down upon the Gentiles. It was because the Mission to the Gentiles have not commenced according to God's timetable. When Lord Jesus had ascended to Heaven, He appointed Prophet Paul to continue His Mission as an apostle to the Gentiles (See Acts 9:1-20). So the Gentiles (Non-Jews) have hope and faith in the salvation plan of God too.
Lord Jesus Messiah appeared to Prophet Paul and appointed him as apostle to the Gentiles (Non-Jews).
Act 9:1 And Saul, yet breathing out threatenings and slaughter against the disciples of the Lord, went unto the high priest,
Act 9:2 And desired of him letters to Damascus to the synagogues, that if he found any of this way, whether they were men or women, he might bring them bound unto Jerusalem.
Act 9:3 And as he journeyed, he came near Damascus: and suddenly there shined round about him a light from heaven:
Act 9:4 And he fell to the earth, and heard a voice saying unto him, Saul, Saul, why persecutest thou me?
Act 9:5 And he said, Who art thou, Lord? And the Lord said, I am Jesus whom thou persecutest: it is hard for thee to kick against the pricks.
Act 9:6 And he trembling and astonished said, Lord, what wilt thou have me to do? And the Lord said unto him, Arise, and go into the city, and it shall be told thee what thou must do.
Act 9:7 And the men which journeyed with him stood speechless, hearing a voice, but seeing no man.
Act 9:8 And Saul arose from the earth; and when his eyes were opened, he saw no man: but they led him by the hand, and brought him into Damascus.
Act 9:9 And he was three days without sight, and neither did eat nor drink.
Act 9:10 And there was a certain disciple at Damascus named Ananias; and to him said the Lord in a vision, Ananias. And he said, Behold, I am here, Lord.
Act 9:11 And the Lord said unto him, Arise, and go into the street which is called Straight, and inquire in the house of Judas for one called Saul of Tarsus: for, behold, he prayeth,
Act 9:12 And hath seen in a vision a man named Ananias coming in, and putting his hand on him, that he might receive his sight.
Act 9:13 Then Ananias answered, Lord, I have heard by many of this man, how much evil he hath done to thy saints at Jerusalem:
Act 9:14 And here he hath authority from the chief priests to bind all that call on thy name.
Act 9:15 But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:
Act 9:16 For I will show him how great things he must suffer for my name's sake.
Act 9:17 And Ananias went his way, and entered into the house; and putting his hands on him said, Brother Saul, the Lord, even Jesus, that appeared unto thee in the way as thou camest, hath sent me, that thou mightest receive thy sight, and be filled with the Holy Ghost.
Act 9:18 And immediately there fell from his eyes as it had been scales: and he received sight forthwith, and arose, and was baptized.
Act 9:19 And when he had received meat, he was strengthened. Then was Saul certain days with the disciples which were at Damascus.
Act 9:20 And straightway he preached Christ in the synagogues, that he is the Son of God.