You can't selectively delete photos from it or even decide what goes into the stream and what not.
Even if you follow the "reset"option by logging into www.icloud.com and click on your username there , this will just empty the cache and instantly add everything back into the stream..
Therefore the only solution is to not use photostream at all if this bothers you. Turn it off on both iOS as well on Mac and PC to avoid stuff being added in the future.
Photostream is no "gallery" or "folder". It just is a real-time flow of everything you ever photographed or saved into the camera-roll. IPhoto/Aperture pick up these "flow" and create folders of them. Due to the limited size in iOS devices, it is only a temporary cache, a virtual "folder" . It will "delete" itself once the photostream feature is turned off.