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Wiktionary
nose-picking

n. (context idiomatic English) Insertion of one's finger into one's nostril, especially to remove mucus.

Wikipedia
Nose-picking

Nose-picking is the act of extracting nasal mucus with one's finger (rhinotillexis) and may include the succeeding action of ingesting the mucus picked from the nose (mucophagy). This action is condemned in most cultures; societies try to prevent development of the habit and attempt to break it if already established. Mucophagy is a source of mockery and entertainment in the media.

However, some scientists argue that mucophagy provides benefits for the human body. Friedrich Bischinger, an Austrian doctor specializing in lungs, advocates using fingers to pick nasal mucus and then ingesting it, stating that people who do so get "a natural boost to their immune system." The mucus contains a "cocktail of antiseptic enzymes that kill or weaken many of the bacteria that become entangled in it", so reintroducing the "crippled" microorganisms "may afford the immune system an opportunity to produce antibodies in relative safety."

Usage examples of "nose-picking".

The ogres stood at attention, but it was obvious that they were not particularly skilled at this, though they excelled at shuffling, spitting, grunting, and nose-picking.