Having operated for many years in the snow with bear paw equipped aircraft, I'm not sure how to answer. I can't recall having anyone ever call me up on the radio to say they had seen something come off my aircraft just after takeoff.
I'm a little curious, do you get this a lot or just once in a while? Most of the passengers I flew in those years tended to be seasoned helicopter users. I don't know if that made a difference.
Nothing leaps to mind as to a fix for this. I kind of suspect it's just something one has to live with if using bear paws.