Ibn Majah

Benefits and Issues:

➊
After eating, one should clean the fingers with the tongue.

➋
Wasting even a small portion of food is ingratitude for the blessing.

➌
It is not appropriate to wipe the hand with a cloth or wash it with water without first cleaning it, because in this way the cloth will be soiled or water will be used more than necessary, and the food particles stuck to the hand will go into the bread, which is a form of disrespect for the blessing of sustenance.

➍
Blessing (barakah) is an intangible and imperceptible thing. For its attainment, one should act upon the teachings of the Prophet (sallallahu alayhi wa sallam) and avoid wasting sustenance.

➎
Letting someone else lick (the fingers) is permissible when the other person does not feel any aversion to it, for example: a wife or children, etc.

Hadith Commentary: Benefits and Issues: When a person begins to eat, most of the food goes into his stomach, some sticks to the vessel, some sticks to the fingers, sometimes some remains in the vessel, and a morsel may fall. Now, a person does not know which part or portion of all these elements of the food contains goodness, blessing, satiation, or becomes a cause for his time and strength. Therefore, he should make use of all these elements and should not leave any part. Even a fallen morsel should not be left lying as it is. From this, it is also understood that only as much food should be put in the vessel as is to be eaten.

Hadith Commentary: Benefits and Issues: This hadith proves that Satan (Shaytan) is always and at every moment lying in wait for a human being. Whenever a person begins any task, Satan tries to ensure that he too has some share in that action. Therefore, by inciting him, he makes the person do something contrary to religious guidance and teachings. For example, when a morsel falls, Satan makes him believe that picking it up is beneath his dignity and considers it a sign of baseness and lowliness. In this way, a person, deceived by Satan’s trick, leaves the morsel for him, and the person does not even realize that Satan’s ploy has succeeded. However, if the morsel falls in an impure place or it is not possible to clean it, then it should be given to a cat or a dog; it should not be wasted, because the Shariah does not permit the wastage of even a trivial thing.

Explanation:
1:
That is, the dust or dirt that has settled on the fallen morsel should be removed,
so that one appreciates this blessing of Allah,
and eats it,
not leaving it for Shaytan, because leaving it would be showing ingratitude for this blessing.
However, it should also be considered that the morsel has not fallen in a place that is impure or filthy;
if that is the case, then it is better to clean it and feed it to an animal.