to peck at

from The Collaborative International Dictionary of English v.0.48

Peck \Peck\, v. i.
   1. To make strokes with the beak, or with a pointed
      instrument. --Carew.
      [1913 Webster]

   2. To pick up food with the beak; hence, to eat.
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            [The hen] went pecking by his side.   --Dryden.
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   {To peck at},
      (a) to attack with petty and repeated blows; to carp at;
          to nag; to tease.
      (a) to eat slowly and in small portions, with litle
          interest; as, to peck at one's food.
          [1913 Webster]