pick at
pick at {v.}
1. To reach or grasp for repeatedly.
The baby kept picking at the coverlet.
2. To eat without appetite; choose a small piece every little while to eat.
He picked at his food.
3. To annoy or bother continually; find fault with.
They showed their displeasure by continually picking at her.
Syn.: PICK ON.
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Source: A Dictionary of American Idioms