The difference between the plain Hebrew and the Aramaic of Targum Pseudo-Jonathan on Exodus 12:23 is the insertion of the Memra — the Word of the Lord. In the Hebrew, God passes over the house. In the Aramaic, the Memra spreads His protection over the door, and the destroying angel is forbidden to enter.
The Targum uses the Memra throughout its rendering as a way to describe God's activity in the world without making Him seem to have physical form. On this night, the Memra stands at the threshold like a sentinel. The angel of destruction has a mandate — the firstborn of Egypt — but it is bounded by the presence posted at the marked doors.
This is a picture of divine justice as a legal act, not a chaotic one. The destroying angel is not rampaging. It is following an exact charter. At marked houses it is barred; at unmarked houses it enters. The blood is the evidence the Memra accepts.
The rabbis emphasized this carefully restrained picture in order to push back against images of God as arbitrary or cruel. On the night of the tenth plague, every boundary is precise. No Hebrew household loses a child because the angel got confused. No Egyptian household is spared because the angel felt merciful. The Memra holds the line.
Takeaway: On the night of the firstborn, mercy and judgment both operated by law. The Word of the Lord was the bouncer at every Israelite door.