Hawkgirl didn't really have much to do and I don't think Gunn knew what to do with her, which is a shame. Giving her a hawk shriek instead of actual dialog was... a choice. She needed more speaking lines.

Personally I thought the shrieking was fun. I do agree she should have had more dialogue and story in general, but the story was already full, so I understand somewhat. Mr. Terrific got a great story beat. Guy Gardner stole a lot of scenes he was in. It would have been nice to give her something more.

And I say "something more" because I do think her dropping the villainous president of the foreign country was a key moment.

We see earlier in the film when everyone is fighting the kaiju that the Justice Gang™ don't have much appreciation for it as a life form. But also they don't have many options.

But when Hawkgirl has the dictator, she absolutely has options. In fact he barely seems bothered as he mocks her. And then she drops him to his death.

We know how Superman would react to that. But what about Gut Gardner? Mr Terrific? Lois's interviews with Superman seemed to imply that actually unilaterally is a problem. Isn't that what the Justice Gang just did? Superman gave him a stern talking to. Hawkgirl killed him.

While this doesn't tell me a lot, it does make me interested in her as a character and keeps me looking forward to wherever she shows up next.