I found that passage. Jesus healed the daughter of that particular dog.
Wouldn't God have known the Jews would reject Jesus? Why send Jesus on a fools errand then?
Do you think no gentile was saved before Jesus?
Yes, when God made Abraham and his descendants the focus of his blessings, here is what was said in Genesis 22
17 That in blessing I will bless thee, and in multiplying I will multiply thy seed as the stars of the heaven, and as the sand which is upon the sea shore; and thy seed shall possess the gate of his enemies;
18 And in thy seed shall all the nations of the earth be blessed; because thou hast obeyed my voice.
Verse 18 is the key verse in understand how God related to Gentiles in the Old Testament, as well as the 4 Gospels.
For the Roman Centurion case, the key verse found in Luke was
3 And when he heard of Jesus, he sent unto him the elders of the Jews, beseeching him that he would come and heal his servant.
4 And when they came to Jesus, they besought him instantly, saying, That he was worthy for whom he should do this:
5 For he loveth our nation, and he hath built us a synagogue.
The Lord Jesus, without hesitation, immediately agreed to his request because he has blessed the Jews, and the Abrahamic covenant allows the blessing to then go to him.
As for the woman, she did not deeds for the Jews but she wisely said in Mark
28 "Yes, Lord," she replied, "but even the dogs under the table eat the children's crumbs." 29 Then he told her, "
For such a reply, you may go; the demon has left your daughter."
Mark has this important detail which I highlighted in bold. That lady made the correct analogy that even the dogs, a term used by the Jews to describe Gentiles, could be blessed with the crumbs falling from the Jewish children's bread. She could have complained to Jesus that he was insulting her but she chose the correct answer by submitting herself to the Jews
Thus Jesus healed her because her faith allowed her to be blessed, thru the Jews, as promised to Abraham.
Perhaps you might understand my point above better by contrasting the above with Jesus approach to Blind Bartimaeus, in Matthew 10
46 Now they came to Jericho. As He went out of Jericho with His disciples and a great multitude, blind Bartimaeus, the son of Timaeus, sat by the road begging. 47 And when he heard that it was Jesus of Nazareth, he began to cry out and say, “Jesus, Son of David, have mercy on me!”
48 Then many warned him to be quiet; but he cried out all the more, “Son of David, have mercy on me!” 49 So Jesus stood still and commanded him to be called.
Then they called the blind man, saying to him, “Be of good cheer. Rise, He is calling you.” 50 And throwing aside his garment, he rose and came to Jesus. 51 So Jesus answered and said to him, “What do you want Me to do for you?” The blind man said to Him, [
a]“Rabboni, that I may receive my sight.”52 Then Jesus said to him, “Go your way; your faith has [
b]made you well.” And immediately he received his sight and followed Jesus on the road.
One can’t help but to notice the contrast in Jesus’s treatment in the two cases of people who exhibited faith. Both the Canaanite lady and Blind Bartimaeus called him the Son of David, which is the proper term for Jesus. Both of them have faith, one might even argue that the Canaanite lady had lesser unbelief than Blind Bartimaeus.
But because the latter was a Jew, Jesus, almighty God, actually stood still and healed him without any hesitation. But the lady, who is a Gentile, had to further go thru so many tests.
My point is not that Jesus was being deliberately cruel to one but kind to other. Like Paul himself stated Jesus’s mission on Earth, he stated in Romans 15 (KJV)
8 Now I say that Jesus Christ was a minister of the circumcision for the truth of God, to confirm the promises made unto the fathers:
As for your last point about gentiles being saved before Paul, yes, as I have explained elsewhere here, gentiles had to be saved thru joining the nation Israel, see
https://christianchat.com/threads/lordship-salvation-vs-easy-believism.195373/post-4407928