Are we talking about the same geese? The ones who hang around public parks and waterways crapping all over?
Plenty of cornfields to hunt them west of Rochester.
The same birds but neither ducks nor geese are “greasy”, as youve said, its in the preparation.
Ducks and geese have a thick layer of fat under the skin of the neck, breast (down to the vent) and all around the tail. This whole area needs to be thoroughly pricked full of holes (No, more. More than that. Do it again.) before roasting to release the fat, which is saved for other uses, and crisp up the skin.
This tendency in geese to develop thick layers of fat was specifically breed for in domestic strains especially those like the dewlap toulouse. With pigs we historically bred for more lard, cows for higher butter fat, and geese for ganzfett or “schmalz”. Wild geese obviously arent intentionally bred for this but its still up to the cook to render out the side product during preparation.