Please be patient and people will eventually answer your questions.

Anytime you try to throw a consumable item like Pheonix Down, a gauge tells you the percentage chance that it'll work. I've tried with Teta and the chance of it working is 0%. In other words, even if it lands square on her, she's incapable of being revived.

It wouldn't bother me so much except the stars over her head are something you see over fallen guest characters and they can usually be revived.