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.