A parasite symbiote is a symbiote that sometimes leaves its host's body after a brutal defeat. They then infect the person closest to them. They will not harm Spider-Man, but if they infect someone, they will attack Spider-Man. They are just as easy to kill as Walkers with one hit.
The only civillian/ally not able to get infected by these are police officers.
To release the Symbiote from their host, keep attacking the Symbiote as much as you can, especially after their health bar is empty.