There is no people of God apart from “the marks” ...

“What then is the significance of seeing the church as the continuation in Christ of God’s faithful Israel?

First, I would offer that it defines us as the community that arises from and is shaped by God’s character. We, no less than Israel, have been called to a distinctive confession that there is “one Lord, one faith, one Baptism, one God and Father of all, who is over all and through all and in all” (Eph 4:17-18). This confession creates as sharp a tension for us as it did for Israel:
So I tell you this, and insist on it in the Lord, that you must no longer live as the Gentiles do, in the futility of their thinking. They are darkened in their understanding and separated from the life of God because of the ignorance that is in them due to the hardening of their hearts (Eph. 4:5-6).
If we read sacred Scripture as the revelation of God’s character in the life of Israel and in the Incarnation of Christ, Israel is a concrete, fleshly, and observable community. While God alone might know who is truly a member, there is no people of God apart from “the marks” that define the church and distinguish it as a faithful witness to God’s character. The Incarnation, life, death, Resurrection, and Ascension of Jesus of Nazareth, son of Abram and son of David (Matt. 1:1) were concrete. The details of His life are as scandalous as the story of Israel. To assert that the God of all creation sent His Son to a remote portion of an empire unprecedented in its wealth to be born to an obscure Jewish maiden is to make a radical claim (1 Cor. 1:22-24).
It means also that the particular expressions of His story entail and impart character to the people who believe and act upon them. Our Lutheran conviction concerning the christocentricity of Scripture means that we will neither add to nor subtract from “the marks” He has given, namely, the prophetic and apostolic witness, the water of Holy Baptism, and the Eucharist.
Though these marks define us, they are more than Yeago’s cultural symbols. They are not historical artifacts or ancient data. They are the real presence of the true God who “call, gathers, and enlightens” people through such sacred means and no other. The incarnational and sacramental character of the church reflects the character of the true God.
The people of God are more than a group of convention-goers who affirm the party’s platform. They are an expression of the one reality sacred Scripture describes, for they have been joined to the Christ in their Baptism, are nourished with His very body and blood, and are directed by His living voice (viva vox Jesu) in the prophetic and apostolic Scriptures.
These definitions and marks do not exist in a fairyland. They cannot be abstracted into a meta-narrative that is either beyond history or locked in the shell of personal religious experience.
Rather, they exist in flesh and blood people who have been joined to a resurrected Lord who was born to the Virgin Mary as Second Adam.
We are not simply witnesses to, but participants in this one, true, saving, and holy narrative, which is visible to the nations all about us—unless, of course, we are so acculturated that the nations see themselves when they look at us.”

THE CHARACTER OF GOD, Dr. Dean Wenthe - Church and Ministry – The Collected Papers of the 150th Anniversary Theological Convocation of the LCMS. PG. 44-46