When I am trimming, I always trim over a scrap piece of batting. then when I am done, I pick it up and throw the scraps in the garbage.
Little threads on my cutting board or pressing board, I just rub my scrap piece of batting over it and it is nice and clean.
When the batting gets disgusting, I just throw it away.
I bet you wonder what I am making... I haven't decided on what the finished product will look like..