פירוש על זבחים 9:5

ואלו אם עלו ירדו – and even if they are kosher and ritually pure. Because the altar is not connected with them at all.

The following if they ascended are taken down:
The flesh of most sacred sacrifices
The flesh of lesser sacrifices;
The remnants of the omer;
The two loaves;
The showbread;
The remnants of meal-offerings;
And the incense.
The wool on the heads of lambs, the hair of he-goats’ beards, the bones, tendons, horns and hoofs if they are attached, go up, because it is said, “And the priest shall turn it all into smoke on the altar” (Leviticus 1:9).
If they were severed [from the animal], they do not go up, for it is said, “And You shall offer your olah, the flesh and the blood, [upon the altar of the Lord your God]” (Deuteronomy 12:27).
Our mishnah lists things that are not meant to be on the altar at all, meaning not in any state. Unlike the things listed in mishnah two, which were once valid and then became invalid, these things were never supposed to be put on the altar. Therefore, even if they were put on the altar, the altar doesn’t sanctify them and they may be taken down.
Sections one and two: The flesh of sacrifices, both most holy sacrifices and lesser sacrifices, is meant to be eaten and not burned on the altar.
Section three: The volume of the omer, offered on the sixteenth of the month of Nissan, was a tenth of an ephah. A handful was burned on the altar and the rest was eaten by the priests. If the remnants were put on the altar, they may be taken down.
Section four: The two loaves that are brought on Shavuot are not meant to be put on the altar.
Section five: The showbread (Leviticus 24:5-19) sat on the golden table in the Sanctuary from week to week. It was eaten not sacrificed.
Section six: Part of the meal offering was put on the altar, but the remnant was eaten by the priests.
Section seven: The incense was put on the inner altar, the one in the Sanctuary. If it was mistakenly put on the outer altar, it can be taken down.
Sections eight and nine: This section seems to be based on a contradiction between the two quoted verses. The verse from Leviticus seems to say that the entire olah is burned on the altar, whereas the verse from Deuteronomy says that only the flesh and blood are burned. The first verse implies that non-flesh and blood parts of the animal, the hair, the bones, sinews etc. are burned, whereas the second implies that they are not. The mishnah resolves this contradiction by stating that when the non-flesh and blood parts are detached from the flesh and blood, then they are not burned on the altar and if they are put up there, they should be taken down. If they are put up there while still attached to the animal, then they have been sanctified and cannot be taken down.

בשר קדשי קדשים – that for eating they exist and not for the altar.

והקטורת – it is not appropriate for the outer altar.

הצמר שבראשי כבשים – we have the reading. But the first clause of the gate is the last, for these bones and sinews that are taught [in this Mishnah], and it is one law for them. The wool that is at the top of sheep, is of a burnt-offering. That the head is not included in the flaying and is offered [in sacrifice] with its hide, and this is what we state regarding the ritual slaughtering of unconsecrated animals [Tractate Hullin 27b], from where do we learn to include the head which was already cut off in the slaughter, that it is not included the flaying, it exists within the burning on the altar, the inference teaches us (Leviticus 1:8): “[and Aaron’s sons, the priests, shall lay out the sections,] with the head [and the suet, on the wood that is on the fire upon the altar].” And there is wool at the height of the head of the sheep near its neck, and similar the hair that is in the beard of the he-goat/wether at the time that they are attached, all of them are burnt-offerings.