@MacZombie - Thank you so much!
To delete images from your iPhone permanently, for Mac users...
Note: Make sure you have imported/backed-up/saved your photos before you do this (because it will delete them forever)
1. Connect your iPhone to your Mac
2. Open the "PREVIEW" software that came with your Mac
3. From the "FILE" menu, choose "IMPORT FROM [the name of your iPhone]"
4. Select which photos you want to delete and hit the delete button (on the bottom left of the window, there will be a red delete icon)
5. Disconnect your Phone from the Computer
6. Shutdown the "PHOTOS" app on your iPhone (To do this: double-click the home button on your iPhone, hold down your finger over any one of the icons that appear at the bottom of your screen until the icons start to shake, then hit the RED MINUS ICON in the top left of the icon) [Note: this will NOT delte the app from your iPhone. It is only shutting it down (from running in the background) so it can refresh / restart.]
7. Then hit the home button on your iPhone again to return to your home screen
8. Open up your photos app and you will see that the photos you deleted are now gone!