I always squeezed the living crap (no pun intended) out of the filter media (sponges, filter socks, sponge filters and etc). Sometime I even take all the bio balls and let it float all over the surface.
Let all the crap spread all over, run the filter until you don't see a whole lot of floating detrious. Once they're gone, they's in your filter now..
I used ALL old water if moving to a larger tank. It makes them feel comfortable to have lesser stress.
You can always do a water change later on LOL
stan