"When the Prophet (ﷺ) ate, he would lick his three fingers, and he said: 'If one of you drops a piece (of food) then let him remove any harm (dirt) from it and eat it, and do not leave it for Ash-Shaitan.' And he would order us to finish (clean) the dish. And he said: 'Indeed you do not know in which part of your food is the blessing.'

This Hadith is Hasan Gharib Sahih.
Jami` at-Tirmidhi Book 25, Hadith 17
← Previous Hadith That the Prophet (ﷺ) said: "When one of you eats food, and he drops a pieces of it, then let him remove anything suspicious from it and eat it. Do not leave it for Ash-Shaitan."

He said: There is something about this from Anas.

Jami` at-Tirmidhi Book 25, Hadith 16 Next Hadith → "My grandmother, Umm 'Asim narrated to me - and she was the slave woman of Sinan bin Salamah - she said: 'Nubaishah Al-Khair entered upon us while we were eating from a large bowl. He narrated to us that the Messenger of Allah (ﷺ) said: "Whoever eats from A Qas'ah, then licks it, the Qas'ah will seek forgiveness for him."

This Hadith is Gharib, we do not know of it except through the narration of Al-Mu'alla bin Rashid. And Yazid bin Harun and others among the A'immah reported this Hadith from Al-Mu'alla bin Rashid.

Jami` at-Tirmidhi Book 25, Hadith 18