Bechorot 3:4 (≈Eduyot 5:6) discusses the case in which the hair of a wounded firstborn animal fell off, then a person put the hair in the window, and then slaughtered the firstborn (or in another version, the firstborn died). Akavya ben Mahalal'el permits using the hair, and the rabbis forbid it.
What's the significance of mentioning putting the hair in the window? I can think of two possibilities:
The reason to put the hair in the window is so as not to accidentally use the forbidden hair of the firstborn along with other permitted hair on the floor. If this is true, the Mishna could just be mentioning putting the hair in the window as an ordinary case. Maybe it even mentions this detail to teach incidentally that it's required to keep the hair separate.
The fact that a person put the hair in the window changes the status of the hair, as it shows that he cares about it. Therefore, there's more of a reason for the sages to declare it forbidden. If he didn't put it in the window, maybe the sages would permit it, or maybe the Mishna is just mentioning this detail to teach that even in such a case Akavya permits it.
Which of these explanations is correct? Or is there another possibility?