They are either looking for tid bits that they like or looking for a nest site.
Birds kept in cages will usually eat sweeter food before the other food. With seed they might prefer the coloured seeds, which are oil seeds, or they might prefer the oats or the millets. Most owners change the seed every day and the birds simply wait for the new seed and then pick out the bits they like and leave the rest. You can prevent this from happening by winnowing the seed. Basically have two containers. Go outside and put the seed in one container and hold that container up about 1-2 feet above the second container. Slowly tip the old seed into the second container and gently blow the seed as it falls. You will remove most of the chewed up seed and husks and leave the good seed in the second container. This can be put back in the cage for the birds to eat. When the birds have eaten 80-90% of the seed, replace it with some new stuff.
Make sure the seed that is left behind is actually seed and not chewed oats. The chewed up oats can be heavy enough not to get blown out when winnowing.
You can put a nest box inside the cage and they might check it out.