First off, Wow, kinda surprised chrome on a '04 would already be oxidizing. Keeping a car outside requires a lot more upkeep than a garaged vehicle (yes, I'm preaching to the choir I'm sure). But seriously, maybe I'm just obsessed but I drove my '02 this past weekend and even though it didn't rain, I buffed the trident and Tubi exhaust tonight 
My best advise would be to use a very fine steel wool on the mesh. That surface is so thin, you won't notice scratches, if it even makes any if you have a fine enough wool. For the trident, replace it... if it were me, I'd even take it in and make my dealer replace the whole thing trident and mesh, if it's rusting. They will probably tell what I'm about to tell you
...take care of the vehicle. Chrome will oxidize over time, there's no stopping it. Pick up a cleaner/protector product from your local Advance Auto. Flitz and MAAS are a couple you could try.
Good luck!
My best advise would be to use a very fine steel wool on the mesh. That surface is so thin, you won't notice scratches, if it even makes any if you have a fine enough wool. For the trident, replace it... if it were me, I'd even take it in and make my dealer replace the whole thing trident and mesh, if it's rusting. They will probably tell what I'm about to tell you
Good luck!