One of the most striking interpretive moves in Targum Pseudo-Jonathan happens quietly on Exodus 12:13. The verse states that the blood on the doorposts will be a sign for Israel, and the Lord will see it and pass over. The Targum slips in a phrase that changes the theology: "the blood of the paschal oblation, (like) the matter of circumcision, shall be a bail for you."
Two bloods, then, protect the house: the blood of the Pesach lamb on the lintel, and the blood of circumcision on the household's men. The rabbis taught that Israel in Egypt had largely abandoned circumcision, and that on the eve of the Exodus they were commanded to undergo it again. The two bloods are wiped on the doorposts together. Both are required for the protection to take effect.
The Targum also clarifies what "pass over" means. The angel of death has been given authority to destroy, but the blood functions as a legal shield — a bail, in the Aramaic — that prevents the angel from entering. This is not God physically leaping over doorways. It is a court-like scene in which the destroying angel's authority is limited by a sign the houses have posted.
For the rabbis, this is why the seder is tied to the covenant of circumcision. An uncircumcised man cannot eat the Pesach (Exodus 12:48). The blood of the lamb belongs to the same covenantal category as the blood of the brit.
Takeaway: It took two bloods to save the house that night. Israel rejoined the covenant before the covenant could rejoin Israel.