As you suggested, I followed the instructions under the heading, "iTunes: Syncing photos." However, I did not find them to be altogether clear. Since I reinstalled iTunes last week, I am pretty certain that I have the latest version. As an example of the opacity, the instructions say: "3. Click the device button in the upper right corner." Upper right corner of what? So, I fumbled around until I opened the "iPhone sync photos" screen. I then went to the instructions under the heading, "To delete synced photos and videos from your device." In order to "delete all synced photos," I selected & then deselected "Sync Photos from." & when the Sync Photos prompt appeared, I clicked the highlighted "Remove photos" button. Although an "Apply" button is not now appearing as I replicate the process, I do recall clicking on an "Apply" button.
Some of the photos may have been removed, but when I open the Photos app on the phone, hundreds remain & when I hover my cursor above the Photos segment of the colored bar at the bottom of the screen, the popup indicates that there are 5500 photos or 5.03 GB. 16.52 GB remain free on a 32 GB phone that I have only been using for a couple of months.
So, it appears that something did not work. I welcome your feedback.