If a face-up "Eyes Restrict" Fusion Monster or "Relinquished" you control is destroyed by battle or card effect: You can Special Summon this card from the GY (if it was there when the monster was destroyed) or hand (even if not). If this card is sent from the field to the GY: You can target 1 "Eyes Restrict" Fusion Monster or "Relinquished" in your GY; Special Summon it. You can only use each effect of "Illusionist Faceless Magician" once per turn.
If relinquished or eyes restrict monster got destroyed, you can special summon this card from either grave or your hand.
The "even if not" part is telling about if this card was not in the graveyard, but instead in your hand, while the monster was destroyed.
Note that some cards could negate effect activation when battle or every phase
Like ancient gear reactor dragon and hydra, GB nerokius, etc