The Western/Moffitt's Canada Goose subspecies that breeds around here is pretty big, around 8-12 pounds, while an Osprey is only about 3-4 pounds. I'm guessing the geese might have felt the need to expand the nest "bowl" somewhat to accommodate their larger size. My guess is that they weren't intentionally dropping sticks. When geese find a nest site, they will lay down and push with their feet to create a depression of the right size, so maybe that caused some of the sticks to fall.
It isn't too uncommon for them to take over the large nests of raptors. It's probably a lot less vulnerable to predation than a nest on the ground, even though the goslings have to take the big leap soon after hatching.
It will be interesting to see if the geese or the Ospreys end up in possession of the nest this spring!
Lisa Millbank