Hestia was careful not to glance back at Tonks, she didn't want to give away her partners location and she wouldn't be able to live with herself if something happened. Instead in one decisive moment, Hestia, ever the Gryffindor, got rid of her wig as smoothly as she could and continued to walk towards them. After all, she wasn't going to get taken in, she had her identification with her and she was a cleared halfblood.
Sure she'd gotten fired from her job, but that didn't mean she was Azkaban bound and maybe, perhaps, she'd be able to help someone.