This is Green Archer’s hidden Noble Phantasm.
Robin Hood was established as an incarnation of nature, and treated as such and celebrated in the May Day festival which succeeded the traditional Celt Beltane Festival (a spring festival).
In the center of the village there are pillars erected called May Poles, and the villagers gather around them and dance the night away. In the May Day festival girls and boys who will soon be of adult age dress up as “May Queens” and “May Kings.”
“May King” especially is a metaphor for Robin Hood.
In this festival the standard costume for May Kings is tight fitting green clothing with brown accents. It goes without saying that this is the green of leaves and brown of tree trunks, so even the costume is designed to emphasize that Robin Hood is an incarnation of nature.
A May King’s attire is said to hide their presence, and allow him to melt away into nature. So Robin Hood essentially has the same ability as the fairy Puck.
This Noble Phantasm is Green Archer’s trump card, and is said to be even more powerful than his Yew Bow Noble Phantasm. It’s a cheat-tier item that makes it impossible to read Green Archers moves, so he completely one-sidedly defeats his enemy.
Robin uses this cloak to hide among the trees, and snipes his enemy from afar like an Assassin.
Since Dan thinks using the Faceless King Noble Phantasm is cowardly, he has forbidden its use outside of combat.
You get to see this skill being used in an unexpected way in CCC, but Passionlip brings that to an unfortunate end.