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Jesus was just teasing when he said:
Mt 15:24 -
But he answered and said, I am not sent but unto the lost sheep of the house of Israel.

And he was sending his disciples on a wild goose chase when he charged them thus:
Mt 10:6 -
But go rather to the lost sheep of the house of Israel.

He/they knew where the house of Judah was, Jesus was a
"Jew"(Judahite) and the disciples were all of the tribe of Benjamin (in whose territory Jerusalem was); the only other Judahite/Jew was Judas.

On the other hand the house of Israel (who were NOT Jews) had been divorced by God (Jer 3:8 - And I saw, when for all the causes whereby backsliding Israel committed adultery I had put her away, and given her a bill of divorce; yet her treacherous sister Judah feared not, but went and played the harlot also.) and dispersed but would become as the sands of the sea, a company of nations.

The tribe of Judah was given the "scepter" or the right to rule but the birthright blessings accrued through all the previous generations went to Joseph(Gen.49:22-26)in double portion form via his sons Ephraim and Manasseh (note also that on these two was conferred the name Israel). (Gen. 48)

Mathew 21;43 Jesus speaking to the tribe of Judah said "Therefore say I unto you the kingdom of God shall be taken from you and given to a nation bringing forth the fruits thereof".

Hardly any wonder why for centuries past the Jews were taught to spit when the name Jesus or Christ was mentioned.