Depends on what the material is...if sponge, then just clean it. If a felt-like material then you can toss it or clean it and reuse (if you're cheap...)
I wouldn't go without the pre-filter, though. It's there for a reason...to keep the bio-balls or other media from getting clogged with that gunk.
There are some bacteria on all of the surfaces of your tank, filter and contents of both. I wouldn't be worried about killing the bacteria on the pre-filter, though. It should be a small part of the total mix.
To clean, you can just rinse and squeeze in running tap water or, better still, afterwards soak in a dilute bleach solution (1 part bleach to 10 parts water). Rinse again thoroughly and then let it dry completely. The chlorine from the bleach evaporates even faster than water. You should have a spare of whatever pre-filter media you have. If its a sponge, buy an extra one and switch back and forth.
(You really don't need to use the wet-dry during your initial rock curing though. A protein skimmer is the best help during this phase. The foamy, gunky mess you're probably experiencing will dissipate in a few weeks and then you can start building up bacteria on the bio-balls as well as the rock. And, of course, some will tell you not to use it at all...)
