pick at in WordNet English dictionary

1. express a negative opinion of
   "She disparaged her student's efforts"
   disparage  belittle  pick at 
   
2. eat like a bird
   "The anorexic girl just picks at her food"
   pick at  peck at  peck 
   
3. pluck or pull at with the fingers
   "She picked nervously at the buttons of her blouse"
   pick at  pluck at  pull at