House of Israel; House of Judah
Two different things. The nation that was united under David and Solomon split in two.
The northern half - Israel - immediately went into idolatry, and after multiple chastenings, and sending them prophets, God divorced them entirely, and used the Assyrians to destroy them to the extent that they did not exist as an identifiable people or nation. They lost all identity and culture and blended into the goyim.
The southern half - Judah - went more slowly astray, having some few kings who listened to the prophets, and reformed the country at least partially. Nonetheless, they went into diaspora and captivity in Babylon. However, they were not divorced or destroyed, as Israel, and retained their identity in foreign lands. Subsequently, the nation was re-gathered and the temple re-built by Cyrus consent.
Jesus ministry was about the restoration of Israel (not Judah). It was prophesied that Israel, who was dead, divorced, and not even a people, would be... revived, reconciled, and in the place where they were called "not my people," they would be adopted as "sons of the living God." That is the thrust of Jesus ministry. He Himself testifies that He was sent to "none but the lost sheep of the house of Israel."
Because Israel was cut off completely, and their restoration required adoption, Israel is no longer party to the covenant at Sinai. They are instead re-grafted under the terms of the covenant with Abram.
This is to their benefit. The covenant at Sinai was largley about punishment, as a result of the idolatry they committed right at the base of Sinai. The monarchy and the priesthood were basically always corrupt, and that is in no small part because they were given for the purpose of executing judgment on Israel.