Dumpster Gang camp items are the loot you haul back to base, and they do not go straight onto a shelf: the burrow holds them between missions, and in the demo the only way to place one is to throw it down.
Dumpster Gang camp items: where stolen goods go
Stolen items are handed in through the burrow hole, which doubles as the mission entrance. That is the same hole you climb into to start a run and climb out of to finish one, so the last act of every mission is also the delivery.
Between missions the gang returns to its camp — the home base with the campfire — where the stolen goods are kept and the place can be dressed up. The loop around the campfire with the crew, sharing the stolen snacks and roasting marshmallows, is the end of a heist.
Getting a heavy haul back to that hole is its own problem, and the heavy loot guide covers the stamina rules.
Placing items in the demo camp
In the demo the raccoons can only throw an item down to place it. Laying out a room is therefore limited to tossing furniture around, and items still bounce away from each other, so a carefully arranged shelf is not something the demo supports.
The developers plan a proper system for managing what you keep in the full release, and say they have something in mind for decorating the hideout as well.
The clear-everything option in the lobby
Talking to the construction hat raccoon in the lobby offers a clear-everything option that empties the hideout — but it deletes everything you have stolen, so it is worth checking your hoard first.
Hats are part of that hoard, and they are the one thing in the game that keeps working after you bring it home. The hats guide covers what they do and why the full game turns them into a one-time unlock.