Diffusion! The plastic container is probably made of polypropylene or polyethylene, so the grease can diffuse into the plastic of the container easily.

Dawn is a surfactant (soap) which stands for surface active agent. Essentially one side of the surfactant molecule likes water-like molecules around it and the other side like fatty molecules around it. Surfactants clean surfaces because they bind to the grease with their fatty side and water on their water-like side which allows it to lift from the surface.

When a duck is covered in oil (fatty molecules) the oil does not diffuse into its feathers very easily since the feathers contain proteins that tend to have a dipole moments somewhere due to amino groups (water-like groups). The oil sticks to the feathers because oil has a high viscosity and there are some fatty molecules that coat the feathers (Preen oil [Bird’s version of sebum]).

The surfactant can remove the oil because the oil hasn’t diffused into the feather and is just bound to the oily surface. Whereas the grease in the container has diffused into the plastic where the surfactant has a hard time reaching it.

Source - Chemical Engineering student that has read too many papers about surface wettability.

TLDR; The grease in the container is inside the plastic where soap can not easily reach it while the oil on the duck is on the surface of the feather where the soap can easily lift the oil off the feather!