This video shows you how to get the relic shield to the gorgon maze as well as what happens after doing so. As soon as you exit the area with the shield it will tell your teammates that the relic has been dropped even though you are still technically holding it.
Extra Info: As soon as I enter the Gorgon area it tells my teammates that the relic has been dropped. They die as a result and I get lost in the Darkness since I am outside of the area (I did not get killed by the Gorgon). From what I can tell Bungie did not intend for the shield to exit the area and thus I don't believe doing anything to the Gorgon's with the shield will cause anything to happen.
*UPDATE*
Here is a new video: https://www.youtube.com/watch?v=nst7XXr_dHU&feature=youtu.be
In this video I do all of the following:
1. Cleanse the island vex time gate
2. Shoot the island vex time gate with the relic shield super
3. Cleanse the tiny hidden cave
4. Shoot the relic shield super in the tiny hidden cave
5. Cleanse other random areas on the way to the Gorgon Maze
6. Shoot a Gorgon with the relic shield
7. Shield smash a Gorgon with the relic shield
8. Cleanse a Gorgon
Please let me know any questions, comments, concerns. I am more than happy to answer anything to the best of my ability.
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And with this video, Tom the level designer lost his job.