You can't actually finish the quest yet. It still tells you to talk to whoever the faction leader is. So I'm assuming on the 15th you'll be able to complete it. Just as it says, you can complete it on a later date.
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Luke Smith already confirmed that the Emblems are for completing PVP activities and are not tied to the quest you've already done....but the OP won't correct his uneducated post because it get's the gullible toddlers to respond....