I say, and with God's success: The impure oil becomes pure if it is made into soap; due to the transformation of its essence into something else. The Prophet Muhammad (peace be upon him) was asked about a mouse that dies in ghee, and he said: "If it is solid, throw away the mouse and what is around it, and eat the rest; but if it is liquid, do not (eat it)." This is found in Sahih Bukhari 5: 2105, and in another narration: "It is beneficial but not eaten," in Sunan al-Bayhaqi al-Kabir 9: 354, and Sunan al-Daraqutni 4: 291. Refer to: Al-Hidayah 1: 37, Fath al-Qadeer 1: 176, Radd al-Muhtar 6: 735, Al-Bahr al-Ra'iq 1: 239, 8: 546, Al-Binayah 1: 755, Risail al-Arkan p. 48, and Fatawa al-Tatarkhaniyyah q. 65/b, and Naf' al-Mufti p. 143, and God knows best.