"Want to try again? Retrace your steps, maybe? Ask if anyone else saw her?"

It's not that Ilda actually believes him, but... it's just like her thing with Yato. She's still not convinced that he's a god, but he's someone in need, and she just can't bring herself to not help. In Eiji's case, she's seen, very clearly, that finding Aifreed was important to him. So what if they'll be spending the next couple of hours searching aimlessly? It's been weeks since she's started helping Yato, and he doesn't have his shrine up yet.