Jesus also extended his minitry to the Gentiles. I'm not understanding why you say He only ministered to the Jews.
Here Jesus is telling this woman that he is only sent to His lost sheep. She is a gentile. Why did he not just heal her daughter right away if he ministered to jews and gentiles?
Mat 15:22 And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, [thou] Son of David; my daughter is grievously vexed with a devil.
Mat 15:23 But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us.
Mat 15:24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
Mat 15:25 Then came she and worshipped him, saying, Lord, help me.
Jesus calls the gentiles dogs twice here
Mat 15:26 But he answered and said, It is not meet to take the children's bread, and to cast [it] to dogs.
Mar 7:27 But Jesus said unto her, Let the children first be filled: for it is not meet to take the children's bread, and to cast [it] unto the dogs.
Eph 2:11 ¶ Wherefore remember, that ye [being] in time past Gentiles in the flesh, who are called Uncircumcision by that which is called the Circumcision in the flesh made by hands;
We gentiles were without God
Eph 2:12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
After the cross, we are now made nigh. We are no longer strangers.
Eph 2:13 But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ.
Eph 2:14 ¶ For he is our peace, who hath made both one, and hath broken down the middle wall of partition [between us];
Eph 2:15 Having abolished in his flesh the enmity, [even] the law of commandments [contained] in ordinances; for to make in himself of twain one new man, [so] making peace;
Eph 2:16 And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:
Eph 2:17 And came and preached peace to you which were afar off, and to them that were nigh.
Eph 2:18 For through him we both have access by one Spirit unto the Father.
Eph 2:19 Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God;