It is best to remove the dead leaves and traps. There are big differences between plants that are growing in the wild and plants that are grown in and around our homes. These cultivated plants are stressed to some degree that their wild brethren are not. Be it light, water, temperature, air quality, etc. When dead matter is allowed to decay in the pots of our carnivorous plants, that matter invites a host of pathogens to have a field day.
Even if a fungus does not appear to be hurting the living tissue, allowed to continue, that fungus will run out of dead matter to feed on and may move onto the living tissue.