If you ask me, the only way to truly solve anything is a good old fashioned sacrifice - we must sacrifice some poor soul(s) in the hopes of ending the incessant rain of plushies. Therefore, my device will be a rather saucy altar.
The altar works primarily as a surface on which to conduct said sacrificing to appease the plushies.
We would need a good amount of Stone to build it, plus some skulls to give the altar a nice uplifting ambience. Some Pure Gold to decorate it all would make the affair more stylish. Last but not least, we need bottles of Grasan Ferment... you just can't carry out a sacrifice sober!
In order to carry this out en masse we'd need a lot of... volunteers constructing altars, providing skulls, and volunteering as tribute. I have enough ferment, so we are fine on that front.
Should the mist continue to manifest afterwards, we could simply drop it in a river. If it floats it is harmless, but if it sinks I would suggest it has been purified by the water, so is no longer harmful.