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Phrase(s): peck at something
1. Lit. [for a bird] to poke someone or something with its beak. • The bird pecked at the ground, snatching up the ants. • I tried to hold on to the bird but it pecked at me hard. 2. Fig. [for someone] to eat just a little bit of something, being as picky as a bird. • Are you well, Betty? You are just pecking at your food. • Please don’t peck at your food. You should eat everything.
McGrawhill's American Idioms And Phrasal Verbs