We have a bunch of parasite tutorial here, linked below 
Yes I personally always recommend killing it with prejudice, or at least trying to and giving it as much grief as you can. I like fire myself. Exorcising is the same an banishing, and if your wards are not good it can come right back.
The point of killing it s not just to get rid of it, it’s that it sends a message out into your field that you’re kind of a mean bugger, and not to mess with you… and you have a lot fewer problems in future. You should have strong wards up anyway, but fewer will test them if they know you’re not a pushover, they’ll go find easier prey.
You probably won’t kill it anyway, it will not like what you do and go away, but it still works like banishing with the bonus intimidation to prevent further nonsense coming your way.
Some of these things are literally like insects, they have no emotions, they only understand strength.