Redditors have discovered a secret in Destiny: The Taken King's Paradox mission and we chart how to unlock it below.
Scan the skeleton during the mission as usual, but with two players in your fireteam. One of you will go to the skeleton, while the other heads for the jumping puzzle and proceeds to the Vex gate outside the throne room. One of the easiest ways to do this from the bottom is with Bones of Eao, which isn't necessary but is recommended.
When all this is complete, do the following:
The third person joining delays the mission end countdown to get the darkness zone; which in order to get a team wipe.
You do not need to be pledged to the FWC. The quest item sits in your Mission items like the Banshee fusion rifles and is to be handed into Lakshmi of the FWC; don't. Handing it in rewards you with faction rep like the fusion rifles, but to your pledged faction instead of Banshee. You also receive the Grimoire Card "Mystery: Praedyth's Door" and five Motes of Light upon turning it in.
The mission is confirmed to be a story node, not a quest.