To what does the "unsightly blemish" refer in Homer's Odyssey?
I think that this question refers to the nineteenth book of Homer's Odyssey. In this book, Odysseus has returned to his palace on Ithaca, but he is disguised as a beggar. At one point, "beggar" Odysseus gains an audience with Penelope. During their conversation, Penelope tells an aged servant, Eurycleia, to wash this beggar's feet. Eurycleia happened to be the woman who had taken care of Odysseus from the time that he was an infant.
In the process of doing this, Eurycleia sees a scar on the beggar's leg that matched the one Odysseus had received while hunting boar many years earlier. When Eurycleia recognizes the scar, she realizes that she is in the presence of Odysseus. Fortunately for Odysseus, Penelope does not hear the old woman's gasp of recognition and Odysseus commands Eurycleia to remain silent about what she knows. The bathing process continues and
Odysseus pulled his stool to the fire to warm himself again, covering the scar with his rags. (A.S. Kline translation)
Later, in Odyssey 24, when Odysseus reveals himself to his father Laertes, he also uses the scar as proof of his identity.
‘See this scar first,’ resourceful Odysseus answered, ‘dealt by the white tusk of a wild boar when I hunted on Parnassus.'
Thus, I think the "unsightly blemish" referred to in this question is the scar Odysseus received while hunting with Autolycus and his sons on Parnassus.