The motives for Petra's involvement here are simple; as a woman of certain status and with a Pandion code of ethics, she has firm beliefs about her duty to those around her. With privilege, responsibility. She acts because she couldn't live with herself if she didn't as much as due to the fact that Taxon's circumstances are changing now and she will move with them lest she be swept away.

None of this means she can't graciously accept thanks.

"Something of this magnitude requires all hands on deck, Master Wayne; I'm glad that mine are useful. I hope there've been no fatalities?"