No need to replace the trunk carpet, topcat has the right idea for you.
You can use an anti-microbial product such as U.S. Microban QGC antimicrobial to control mold, mildew and odor associated with water damage. This is an EPA registered product that dilutes down for economical use, you can clean hard surfaces as well as the trunk rug too. I sell alot of Microban QGC to the professionals that shop the equipment store I manage, look for a professional carpet cleaning supply store in your area.
The trunk rug is mostly synthetic olefin based, water usually wont hurt it but don't "scrub the heck" out of it, you'll cause nap distortion, air dry over a fence, it'll be dry in a couple of hours.
Any trunk rust?
edit, should nver try to spel before I have first coffee,,,
QGC is one of the very best water remediation products out there for odor and disinfecting, I have used it in my Fiero's hvac system after a little rodent died in there, crawl space musty odor, bathroom pipe burst, mildewed basement.
[This message has been edited by jetman (edited 08-02-2009).]