So, this might muck things up a bit, but for the sake of complete and accurate information, the "Holy Mage Only" restriction does prevent a few things other than just including it in your spellbook. Per the Supplement, this restriction prevents a non-Holy Mage from including the spell in their spellbook, casting the spell during the game, or controlling the spell during the game.
That said, Arkdeniz's answer is still correct. Familiars essentially check back with their Mage regarding Mage restrictions. Think of them as an extension of the Mage, casting the spell on behalf of their Mage. So, Holy Mage Only is not a problem for Cassiel. But the subtypes of Eye for an Eye are. She can't cast it because it's neither Healing or Protection.
