"This item has a faction modifier." Casting identify while holding this item on the cursor shows which faction is modified:
[Wed Aug 16 22:04:53 2017] You begin casting Identify.
[Wed Aug 16 22:04:53 2017] Your Silvery Mask begins to glow.
[Wed Aug 16 22:04:56 2017] Item Lore: Blessed by the Council of Six.
[Wed Aug 16 22:04:56 2017] This item gives positive faction to Circle of the Crystalwing.
Note that you have to be wearing this cloak for the faction modifier to take effect. It's not the illusions that come from it that provide the faction modifier (though the illusions may possibly have innate racial faction modifiers, those would be separate).