All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Istinjaa'is to clean oneself after defecation with water or tissue. Yet, making Istinjaa' isn`t required save when filth is discharged from one of the two private parts. Moreover, some jurists are of the view that making Istinjaa' in case of farting is reprehensible since doing so will lead to exaggerations and whispers. In addition, Al-Imam An-Nawawi (May Allah have mercy on his soul) said (What means): "The majority of Muslim jurists are of the view that making Istinjaa' due to farting, sleeping, touching penis or touching women in which touching them renders one`s Wudu` invalid isn't recommended." [Al-Majmoo' vol.2/pp.113], for further details in this regard, kindly refer to [Tohfat Al-Mohtaj vol.1/pp.185] and [Mughni Al-Muhtaj vol.1/pp.166]. And Allah Knows Best.