Preparing the Passover sacrifices required careful organization and a strict separation between the sacred portions destined for the Altar and the meat meant to feed the families of the nation.
The primary approach among commentators is that the removal of the burnt offering during this event does not refer to a standard sacrifice that is entirely consumed by fire. Instead, it describes the extraction of the fats and internal organs from the Passover lambs. These specific parts were known by this title because they were the portions designated to go up in smoke upon the Altar.
This careful separation served two purposes. First, the edible meat of the Passover lambs was divided and distributed among the various family groups [מצודת דוד, מלבי״ם, ביאור שטיינזלץ]. Adding a practical layer to this distribution, [רלב״ג] explains that the cuts of meat were handed out in a highly organized manner to the members of the household present that day, with each person receiving a specific, known portion until everything was shared.
The second purpose of the separation was to present an offering to God. The fats and organs that had been removed were handed over to the priests, who then placed them on the Altar [מצודת דוד, מלבי״ם].
This exact same method of preparation was applied to the cattle brought as festival peace offerings. Just as with the Passover lambs, the internal fats were first extracted and given to the priests for the Altar, and only afterward was the remaining beef returned to the owners for their holiday feast [מצודת דוד, ביאור שטיינזלץ].