It was taught in another source. Rabbi says: One verse states, "And the priest shall offer the whole" (Leviticus 1:13) — an inclusion; and it is written, "And you shall offer your burnt offerings, the flesh and the blood" (Deuteronomy 12:27) — a limitation. How then? While joined, let them go up, and so on. And the Rabbis hold: "joined" did not need to be included, just as it is with the head of the burnt offering; rather the verse was needed for what separated. And Rabbi holds: parts joined that are permitted did not need a verse to include them; rather the verse was needed for the displaced sinew while attached. And the Rabbis say: that you cannot say, for "from the drink of Israel" (Ezekiel 45:15) means from what is permitted to Israel. And Rabbi says: it is like the forbidden fat and the blood. And the Rabbis say: their commandment is precisely so, which is different. Rav Huna said: The displaced sinew of a burnt offering — he removes it onto the ash heap. Rav Chisda said to him: Is it written "therefore the altar shall not eat it"? It is written, "therefore the children of Israel shall not eat" (Genesis 32:33). And Rav Huna replies: "from the drink of Israel" — from what is permitted to Israel. And since he removes it, why does he bring it up at all? Because it is said, "Offer it now to your governor" (Malachi 1:8). It was taught in accordance with Rav Huna: the displaced sinew of a peace offering he sweeps into the channel, and that of a burnt offering he removes onto the ash heap.
What Becomes of the Displaced Sinew in the Burnt Offering
Yalkut Shimoni on Torah 445:2
תַּנְיָא אִידָךְ, רַבִּי אוֹמֵר כָּתוּב אֶחָד אוֹמֵר (להלן פסוק יג) "וְהִקְרִיב הַכֹּהֵן אֶת הַכֹּל" רִבָּה וּכְתִיב "וְעָשִׂיתָ עֹלֹתֶיךָ הַבָּשָׂר וְהַדָּם", מִעֵט, הָא כֵּיצַד, מְחֻבָּרִין יַעֲלוּ, וְכוּ'. וְרַבָּנָן מְחֻבָּרִין לֹא אִצְטְרִיךְ לְרִבּוּיֵי, מִידִי דַּהֲוָה אַרֹאשָׁה שֶׁל עוֹלָה, כִּי אִצְטְרִיךְ קְרָא לְפָרְשׁוּ וְרַבִּי, מְחֻבָּרִין דְּהֶתֵּירָא לֹא אִצְטְרִיךְ קְרָא לְרַבּוּיֵי, כִּי אִצְטְרִיךְ קְרָא לְגִיד הַנָּשֶׁה בִּמְחֻבָּר וְרַבָּנָן הַהוּא לֹא מָצִית אָמַרְתְּ (יחזקאל מה, טו) "מִמַּשְׁקֵה יִשְׂרָאֵל" מִן הַמֻּתָּר לְיִשְׂרָאֵל, וְרַבִּי, מִידִי דַּהֲוָה אַחֵלֶב וְדָם וְרַבָּנָן, מִצְוָתָן בְּכָךְ שָׁאנִי אָמַר רַב הוּנָא גִּיד הַנָּשֶׁה שֶׁל עוֹלָה חוֹלְצוֹ לְתַּפּוּחַ אָמַר לֵיהּ רַב חִסְדָּא מִידִי כְּתִיב עַל כֵּן לֹא יֹאכַל הַמִּזְבֵּחַ, (בראשית לב, לג) "עַל כֵּן לֹא יֹאכְלוּ בְּנֵי יִשְׂרָאֵל" כְּתִיב וְרַב הוּנָא "מִמַּשְׁקֵה יִשְׂרָאֵל", מִן הַמֻּתָּר לְיִשְׂרָאֵל. וְכִי מֵאַחַר שֶׁחוֹלְצוֹ לָמָּה מַעֲלֵהוּ, מִשּׁוּם שֶׁנֶּאֱמַר "הַקְרִיבֵהוּ נָא לְפֶחָתֶךָ" תַּנְיָא כְּוָתֵיהּ דְּרַב הוּנָא גִּיד הַנָּשֶׁה שֶׁל שְׁלָמִים מְכַבְּדוֹ לְאָמָה וְשֶׁל עוֹלָה חוֹלְצוֹ לְתַפּוּחַ.