Komentarz do Rodzaju 37:23

את כתנתו HIS GARMENT — this means his shirt.

את כתונת הפסים, the only reason why these words have been inserted here is to remind the reader of what had been the cause of the entire tragic episode of fraternal hatred. However, if the Torah had not added these words, we would have been misled. The fact that the Torah describes the brothers sending the blood-spattered tattered remains of this tunic to their father (verse 33) was designed to deceive their father into believing that what happened to Joseph had nothing to do with his father having had this garment made for him and the brothers having resented this. The Torah does not want us, the readers, to be misled as the brothers had succeeded in misleading their father into thinking that he had become the victim of a wild animal.

ויפשיטו את יוסף את כתנתו, They stripped Joseph of his tunic, etc. According to the plain meaning of the verse the word כתנתו refers to his shirt, whereas the additional words את כתנת הפסים refer to his outer garment, the one his father had made for him. In order to understand the verse thoroughly we have to know why the Torah did not write ואת כתנת הפסים, "and the striped coat."