It was nice of Green Lantern to give her a window to look out of while she's trying to think of a way to escape. It shouldn't take her that long, you don't have to be a genius to figure out a six foot stack of sticks isn't going to hold somebody who can become 200 feet tall. I don't know what that makes Giganta, but I'm guessing the reason she doesn't wear shoes is because she can't figure out how to tie them.