How nice! Sorry I don't have an answer but did the finch ever ran into the real parents?

When I lived in the Northwest Territories it was really hit and miss for a successful nesting season for tree swallows. If cold, rainy weather persisted for a few days, the birds would abandon their nests to forage further afield for insects. This could happen any time during the season and it was often a little heart wrenching to clean out the nest box in the fall and find five beautifully fledged out young, all dead. The parents were forced to abandon them in search of food. As for their fascination with the chickadee house I cannot offer any explanations or advice. Who knows what goes on in the brains of birds?

If these are tree swallows, the babies immediately fly away when they fledge. They don't land on the ground. I've had tree swallows successfully nest for three years in a row. This year something happened to the mother and I found her dead in the nest box and the eggs never hatched. About 2 weeks after they hatch the babies are ready to fly. They are excellent flyers and they just leap out of the box and are gone. They return to the yard the same day a few times and then you never see them again. The parents leave as well once the young have fledged. Tree swallows also nest in boxes or cavities, not open nests. So if there was no nesting box nearby, they probably aren't tree swallows; maybe a barn or cliff swallow. I don't know the the fledging habits of barn or cliff swallows.

Neat! That little beak is just waiting for another bug/worm.