Saeril noticed the amount of caution that everyone had displayed towards her, and all she could do was look away from them, not willingly to hold eye contact with them for too long. In all honesty, she was quite used to such reactions, but with the addition of the people she had treasured, to do the same, she was not so used to that. Even Gandalf noticed the change and, with Frodo to look back at him with the same expression, he reassured the young Hobbit with a nod, silently telling him to trust her, as well as himself. Plus, he had full-faith in the winged she-elf, knowing what really happened when he confronted her, temporarily healed her, and gave her sanctuary, in the first place. 

Even with young princess to decide on joining them on the task, the Grey Wizard winked to the Lord, really to reassure him that everything was going to be alright...even though he can't really be sure that the promise was guaranteed. However, Gandalf had complete faith in the girl, as he had managed to sense some potential within her, since she was a child. 

"And you have my bow", Legolas spoke up, having to stand with the others, besides Tauriel and Yavanna.