On my Stats page, recent activity shows I completed the Dust Palace strike on 9/20, and the Undying Mind, Shield Brothers, Sunless Cell, and Fallen S.A.B.E.R. strikes 9/21, all utilizing the strikes playlists (Dust Palace in Heroic, the others in the standard playlist).
In the grimoire Activities/Strikes page, all those cards have unlocked except the Dust Palace and the Undying Mind - maybe because I am on Xbox One and they were previously Playstation Exclusives?
https://www.bungie.net/en/Grimoire/1/4611686018430473914/Activities/Strikes?_unlocked=False
Looking at the stats for the enemies in those strikes (all of which have unlocked in the grimoire), some show kills and some do not, but failing to land a kill shot shouldn't coincide with the activity being unlocked, should it?
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Anybody figured out how to unlock dust palace yet ?