I think im having this exact issue. Where did you find the Battleye window? and how did you go about unblocking the extension?
English
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When I was disconnected from interent and started Destiny, Steam window popped up that synchronization could not be completed and if I want to still continu. I pressed yes and then BattleEye window popped up (BE always starts up first when you want to play Destiny) and in this window was information about blocked file. After this I just connected internet back, turned off the extension and that was it.