It would be useless to try and change Galadriel's mind when she appears in such a mood, but perhaps the blood loss isn't making her think clearly, so Ellana takes a healing grenade from her belt. She's never been much of a healer herself, so she comes prepared.

"All right, we will search." She breaks the grenade on the ground to let its healing mist work on her friend. "But it'll be pointless to look if you collapse from blood loss first. Please, give this a moment to work and tell me what you remember when you came back through. Maybe there's a clue; something you didn't notice at the time with demons everywhere, but it'll help us find it." Because she doesn't want to leave a powerful magic ring on the ground for anyone to find any more than Galadriel does.