Looking on my IPhone it is called Photo Stream (not My Photo Stream) and says "113 from My Computer". However, I have cleared the Pictures folder in Mac HD and none of these photos exist on my laptop so they are residing wholly and solely on the IPhone. The same photos (113 of them) also reside permanently on my IPad. I am running the latest IOS7 for IPhone and IPad. No matter what I try to do to access "Photo Stream" there is no ability to delete these photos out of both devices. Photos and Photo Stream are turned on both devices and ICloud is active so not sure what to do.
If it were the regular Photo stream, the album would be called "My Photo Stream", so it is not rhe Photo Stream you are looking at, but a regular album or an album syned from your mac.
Have you ever synced the iPhone and iPad wit your computer using iTunes? This really looks like the album "Photo Stream" is an album that has been synced to your iDevices using iTunes. Then they can only be removed by syncing again with iTunes, selecting to sync photos, but deselecting all photo albums in iTunes.
If it is a regular album, however, try to find the photos in your camera roll and delete them there. Then they will also vanish from the album. And photos, that have been edited, cannot be deleted at all, unless you revert them to original.