While TuneUp is Attached, it will respond and "follow iTunes" for many window and application commands that you apply to iTunes, such as the Close, Minimize and Zoom buttons in the Title Bar: 

You can "Close" TuneUp while it is Attached to iTunes, but Minimize and Zoom are disabled on TuneUp, as they aren't necessary... TuneUp will "follow" the Minimize and Zoom states of iTunes in order to maintain its Attached mode.

Quitting or Closing iTunes while TuneUp is attached will also Quit TuneUp, as TuneUp requires iTunes in order to operate properly.