Azaar immediately turned the ship around to search for Mira, but he wasn't all that hopeful. They were only able to chase after Hana because she was just a mortal, and the pendant she always wore released a particular aura.
As long as they were in Hana's general vicinity, they'd be able to sense this aura.
Of course, Hana could just drop the crescent moon pendant somewhere so she wouldn't get caught, but that's pretty much the last thing she'd want to do.
For one, Azaar and his family would still find it, and since she's only a mortal, she'd be unable to create enough distance between herself and the pendant before she got caught.
She might have her impeccable stealth skills, but as a mortal, there are only so many places she can hide in the mountains without getting killed. Additionally, her stealth skills are only at their full potential when she's standing still.