CONTAINS SPOILERS

Once you attach a Parasite to your body, there's no immediate way to detach it until you discover a Parasite Extractor. It detaches a Parasite and gives you Obolites. The first time you can access one is by defeating the first boss. After the battle, the Parasite Extractor can be used in the next room. Note: There are consumables that can detach Parasites as well.