My stats show I've completed 121 strikes, yet at the top of my "closest bonuses", "Strikes Introduction" is stuck at 42. It showed 42 yesterday, after which I did both the heroic, nightfall, and around 5-6 tiger strikes. It appears the strike grimoire card bonus is not giving credit for the strikes completed in the Vanguard Strike Playlist or the weekly Heroic/Nightfall strikes.
Edit: Still getting likes and replies on this post so figured I'd post an update. 4 months later, stats show 300+ strikes across 3 characters (add 150+ from one deleted character) and my grimoire progress strike total is only up to 122.
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The vanguard strikes don't count and the weekly and nightfalls you have to do the normal strikes and if you have a full fireteam it counts for three strikes toward your grimoire per strike, and no it's not a glitch like some bonehead was saying on the comments.