(basically, hacking some CSS rules by creating a file in your AppData directory, so that the top bar is hidden)
Incidentally, I also discovered that Tree Style Tab's settings page under Firefox has a nice little box where you can configure the CSS it uses, which was nice because I prefer it with a smaller font and less padding.
What uglycoyote commented is the stopgap solution for now, but an API for doing that is in the works, so in a few versions from now, you shouldn't need that more-or-less hack anymore.