peck up
Of a bird, to peck something in order to eat it. A noun or pronoun can be used between "peck" and "up." I love scattering seeds on our back porch and watching all sorts of different birds come by to peck them up. A little finch hopped over and began pecking up the crumbs from our sandwiches.
peck something up
[for a bird] to eat something up by pecking at it. The chickens pecked all the grain up. The birds pecked up the grain.