“Remember that you were formerly gentiles in the flesh — called the uncircumcision by those called the circumcision in the flesh by hands — that you were at that time without Christ, alienated from the citizenship of Israel and a stranger to the covenant and the promise, being without hope and an atheist in the world.”
The contrast between the Old Testament administration of the mark of the Covenant and the New Testament administration of the mark of the Covenant are profound. The first was made with blood and only on the males. With the bloody sacrifice of Christ being complete, the bloody mark of circumcision is replaced with the bloodless mark of baptism, also shifting from a mark on the body to a mark on the soul. The fleshly one being made with human hands but the spiritual one, though through human agency, being made by God himself. In this case, Paul is addressing a largely gentile audience and pointing out that this salvation that God has worked is doing more than just giving them salvation from their sins; it brings them into the covenant of God and the promises that are found within it — it makes the gentile a citizen of the holy city of Christ.
And so, a second change is being highlighted to these Ephesian Christians. Not only is there a different way that the covenantal mark or sign is applied, there is a different way that citizenship is received (and note that citizenship in the Roman world was very difficult to receive and was highly valued). Now it is no longer a contrast between Israelites and those outside of Israel. Now it is those who are in Christ and those who are not in Christ. With Christ comes membership in the covenant, citizenship in heaven, and the promises which bring hope.