I disagree with your interpretation of Jesus' reference. Jesus was commissioning outreach to the Gentiles worldwide.
Mark 13:10 tells us that before the end arrives “The gospel must first be preached to all the nations,” while Mark 14:9 concludes the story of the anointing at Bethany with “Wherever this gospel shall be preached throughout the whole world, what this woman hath done shall be also told, in memory of her,” and it seems unlikely in the extreme that the author intended only a world-wide outreach to Jews. By the time of John’s gospel, the issue is settled: John 1:29 has the Baptist saying “Behold the Lamb of God which taketh away the sin of the world;” John 3:16 admonishes that “God so loved the world that he sent his only begotten Son;” John 10:16 quotes Jesus as desiring to bring the “other sheep” into the one flock; John 12:20-21 has Greeks asking after Jesus; and so on.
What God said via His Old Testament prophets gives more detail of what would happen with His scattering of the ten lost tribes of Israel. Most of my Christian brethren don't read those prophecies that are in the Old Testament prophets, like Hosea.
Some churches even wrongly teach that the Old Testament is dead history when it contains many prophecies still not yet fulfilled to this day. By their wrongly doing that they actually are creating a different religion with only teaching The New Testament.
The following is God declaring what He would do to the ten northern tribe kingdom. The final verse here in Hosea 2 Apostle Paul quoted in Romans 9:25-26 to Roman Gentile believers on Jesus Christ. Yet the Book of Hosea was originally given only to the ten northern tribes of Israel when God was getting ready to end their northern kingdom for their continuing to do false worship.
Hos 2:14-23
14 Therefore, behold, I will allure her, and bring her into the wilderness, and speak comfortably unto her.
In the previous Hosea 1 Chapter and earlier Hosea 2 verses, God had established the northern ten tribe "house of Israel" as having fallen away from Him into Baal worship, and He determined to scatter them.
The above verse is God proclaiming what He would do to the ten tribes after scattering them "into the wilderness", which historically was to the West, in Asia Minor and Europe where The Gospel was preached after it was rejected in Jerusalem by the Jews.
15 And I will give her her vineyards from thence, and the valley of Achor for a door of hope: and she shall sing there, as in the days of her youth, and as in the day when she came up out of the land of Egypt.
16 And it shall be at that day, saith the LORD, that thou shalt call Me Ishi; and shalt call me no more Baali.
17 For I will take away the names of Baalim out of her mouth, and they shall no more be remembered by their name.
The ten tribes of Israel had fallen into Baal worship. But at this point, once God scattered them, He would take the names of Baali out of their mouths, and they would begin to call Him "Ishi" (i.e, my husband - see 2 Cor.11).
18 And in that day will I make a covenant for them with the beasts of the field, and with the fowls of heaven, and with the creeping things of the ground: and I will break the bow and the sword and the battle out of the earth, and will make them to lie down safely.
19 And I will betroth thee unto Me for ever; yea, I will betroth thee unto Me in righteousness, and in judgment, and in lovingkindness, and in mercies.
20 I will even betroth thee unto Me in faithfulness: and thou shalt know the LORD.
That is about the scattered ten tribes of Israel here eventually being scattered among the Gentiles and along with believing Gentiles, and likewise receiving The Gospel of Jesus Christ with them. A small remnant of scattered Jews would also receive The Gospel with them, and they all would become Christ's Church.
21 And it shall come to pass in that day, I will hear, saith the LORD, I will hear the heavens, and they shall hear the earth;
22 And the earth shall hear the corn, and the wine, and the oil; and they shall hear Jezreel.
23 And I will sow her unto Me in the earth; and I will have mercy upon her that had not obtained mercy; and I will say to them which were not My people, "Thou art My people; and they shall say, 'Thou art my God.'"
KJV
Apostle Paul quoted the above verse in 'red' in Romans 9 when he was speaking to Gentile Roman believers on Christ. That meant Paul was including the ten northern tribes of Israel in with the Gentiles in the West with accepting The Gospel of Jesus Christ. Even in the Scottish Declaration of Arbroath those Scots proclaimed their heritage from old Israel.
