But He answered and said, “I was not sent except to the lost sheep of the house of Israel.”
Matthew 15:24
House of Israel is not Abraham's descendants just because born according to the flesh, as the definition of those who are 'of Israel' are those who are as Issac was born according to the promise of God's Spirit.
6 But it is not that the word of God has taken no effect. For they
are not all Israel who
are of Israel, 7 nor
are they all children because they are the seed of Abraham; but, “In Isaac your seed shall be called.” 8 That is, those who
are the children of the flesh, these
are not the children of God; but the children of the promise are counted as the seed. 9 For this
is the word of promise: “At this time I will come and Sarah shall have a son.”
So to be 'of the House of Israel' is more than just living as if you were, like Christ says it here, they make a false claim that God is their Father in John 8, But prove God is not by their desire to Kill Christ the Son and also that they don't believe in Christ.
40 But now you seek to kill Me,
54 Jesus answered, “If I honor Myself, My honor is nothing. It is My Father who honors Me,
of whom you say that He is your God. 55 Yet you have not known Him, but I know Him. And if I say, ‘I do not know Him,’
I shall be a liar like you; but I do know Him and keep His word. 56 Your father Abraham rejoiced to see My day, and he saw
it and was glad.”
57 Then the Jews said to Him, “You are not yet fifty years old, and have You seen Abraham?”
58 Jesus said to them, “Most assuredly, I say to you, before Abraham was, I AM.”
Satan is their father, not God, So they are not really of the house of Israel, they are liars.
40 But now you seek to kill Me, a Man who has told you the truth which I heard from God. Abraham did not do this. 41
You do the deeds of your father.”
Then they said to Him, “We were not born of fornication; we have one Father—God.”
42 Jesus said to them,
“If God were your Father, you would love Me, for I proceeded forth and came from God; nor have I come of Myself, but He sent Me.