personally, remove it.
I did it with mine. I then pressure washed it, actually that's a standard for me and every single car I've owned. even the toughest car I've done haven't deterred me from keep doing it again and again.
you'd be surprised of what is in there.
if you decide to do it make sure to visit a local hardware store and buy foam padding from the carpet dept. make a pattern out of the old one glued to the carpet. the multicolor padding one is ok. when you remove the carpet discard the original padding, you need to yank it out, that is where ALL the creepy stuff is at, bacteria and bad smell. once you PW the carpet let is dry. hang it from some high place so it drains completely. do not let it dry out laying it over the floor.
when installing the carpet use the new carpet padding the same size as the old one. trust me the carpet will be cleaner, no creepy smells or anything and above all a very nice cushioned floor.
the toughest part is to remove the part under the console. I cut (split) one single piece and so far the carpet still looking factory. it doesn't affected how the carpet sits so that worked fine fore me.
gl