It appears that these photos were synced from your computer, possibly via iTunes. If that is the case, the only method to delete these photos is via iTunes and the computer. Connect the iPhone to the computer, open iTunes, select the iPhone and then go to the Photos tab. Unselect the folder/album name and then sync the phone again. That will delete the photos.
Photos synced from the computer can only be removed via another sync.
Thanks much. I'm sure this is the explanation. I just got an iphone this year and I'm sure it happened when I was playing with ways to get photos off the phone and onto my computer. Syncing is confusing to me, I think mostly because I don't know how to discriminately "sync" and even though I have an iCloud account I haven't really figured out how to control it and control what does and doesn't sync. I did though find that moving photos from iphone to computer seemed hard and I use a very easy app for this now called WiFi Transfer and it in a snap downloads all the photos I want to a zip file from iphone to my computer through a web browser on the computer.
Thanks. I look forward to getting rid of the unwanted synced album.
I tried this and it did not work. When I connect my iphone and look at it in iTunes under the photo tab it says zero photos. I don't see anything to delete. Under the name of the album in my "Events" on my iphone does say 15 from my Mac. And there are 15 photos in the folder. I can' delete any of them. I went to my iMac and deleted all of the photos in iPhoto because I don't use iPhoto. I thought that would help. I don't know how to get rid of this "event" in my photos on iphone.