It's highly unlikely that the pheasants are the source of your problems. I've never seen anything on wild pheasants which I've handled. In fact, when I worked on a game farm, with 35,000 birds through in a season, I never saw any parasites on them.
Dust bathing is how wild birds keep themselves free of parasites. If your hens can find a dry spot they will create a deep hole in which they will bathe daily. If you feel inclined, you can tip a bit of louse powder into the bathing hole and that will help.