Komentaryo sa Exodo 24:8: Rashi, Rabbeinu Bahya, Chizkuni & Tur HaArokh

ויזרק means sprinkling — he sprinkled it on the people (not he threw it against the people, as this word might imply; cf. e. g., Exodus 9:8: וזרקו משה השמימה). The Targum, however, renders it by: and he poured it (the blood) upon the altar as atonement for (על) the people, adding the words “upon the altar”, and taking על העם to denote “on behalf of the people”, i. e. he poured it out to atone for the people.

ויקח משה את הדם ויזרוק על העם, “Moses took the blood and sprinkled it on the people.” He sprinkled the blood on them in order to enable them to enter the covenant with G’d by means of blood. The bloodstain which remained on each of their garments was called עדי, “jewel, ornament,” as this stain was a sign of distinction and honour for them. It served as testimony that they had entered into a covenant with the Lord. This is the reason why after they had sinned at the golden calf, i.e. had violated that covenant, G’d told Moses to tell the people to remove עדיך, “your jewelry.” G’d meant that the people were to take off the garments with that bloodstain which so far had served them as jewelry. When we read in 33,6: “the Children of Israel were stripped of their jewelry,” this means that they divested themselves of the garments they had worn at the time of the revelation.
Why did G’d employ blood as the instrument by means of which He made the covenant with the people? it was a hint that as long as the Israelites were to be loyal to the covenant and they would observe the commandments all well and good; if they were to fail to do so G’d would permit their blood to their adversaries. This is the view of Rabbeinu Chananel

Rashi writes in a similar vein saying that Moses sprinkled part of the blood on the clothing of the Israelites as a sign of distinction similar to when he had been told to sprinkle blood on Aaron, his garments, and Aaron’s sons and their garments at the time they were being consecrated as priests (Exodus 29,21).
Onkelos appears to understand the words על העם, which he translates as על מדבחא לכפרא על עמא, “on the altar as atonement for the people,” as meaning that the word על does not mean “on” but “on behalf of.”