I made one post already about how doing vanguard strikes does not count toward your total number of strikes in grimoire, but that doing the regular strikes from the planet does. But to add to that I also noticed today that it counts the strike by the number of people in the fireteam at time of completion. So when I had 2 other people with me it counted for three strikes, and when someone left early and the last spot wasn't filled before beating the strike it counted the strike twice for me (or just once if both other players left). Just thought I'd point this out in case you weren't aware.