What exactly came with your terrarium? When you say "a lot of them" are you talking about traps? But you also mention a pitcher plant. Is this a terrarium with mixed CPs in it?
As stated, you can cut off any dead (brown or black) parts but leave anything that is green. Even though CPs eat bugs, they get their main food supply from photosynthesis like any other plant. So the more green, the more surface area to make food.
If its traps on a flytrap that are black, cut them off. They only live for a while and then die off anyway so don't worry. They will continue to grow more leaves (although their dormant period is approaching).
If you have mixed CPs, you will need to know what kind of plants you have to distinguish between what might need dormancy (flytraps and Sarracenia for example) and what does not need dormancy (a tropical sundew for example).
Anything that is covered in dirt will not be damaged if you take a spray bottle and spritz it to clean it off to find roots. Just make sure, as with all CPs, that your water is PURE (distilled, rain or reverse osmosis water).
Congrats on your new plants.