What I didn't say (but meant to) is that carbon only works for a very short time. If you can cut a slit or 3 & remove most of it, it'll probably be easy to rinse & squeeze out.
If the carbon has been in for a while, it is also a great bacterial filter media.. so tossing it will result in a list of bacteria more so than rinsing under the tap.
If you are going to ditch it, ditch it but don't clean the filter after for a week or two.. just in case.
