I don't think we have the option of chosing what photos we will keep in the Photostream folder. Deleting them with iExplorer (a program that you install in your Mac) doesn't work because the photos are stored in iCloud.com. So to delete "all" photos you have to do the following:
1) on your iPhone go to Settings >> Photos and turn "off" Photo Stream. It will tell you that all photos will be deleted from you iPhone device. Don't turn it back on again.
2) Acces your account at iCloud.com
3) When logged in you will see your name at the top of the page on the right, click on your name. Click on the Advanced option and then click on the Reset Photo Stream button. That's it.
4) Now you can go back on you iPhone Settings >> Photos and turn "on" Photo Stream.
Now all your unwanted and wanted photos are gone.
Sorry there is no option to delete only the unwanted photos at least for now.
Hope this helps! It did for me.