Hello there RLWidman,
Thanks for posting here on the Apple Support Communities! This is a place where other Apple users can submit questions or respond to others to help lend a hand. Let's take a closer look as we do our best to provide some additional insight.
It looks like you may be in the wrong place to edit the photos you've set there. In the System Preferences > Desktop & Screen Saver > Desktop section, what you see in the left column are actually folders on your Mac. You'll need to locate that folder in Finder and then remove the photo from that specific folder in the Finder instead.
More about this is explained here: Change the desktop picture (background) on your Mac
Add a folder of your own images
To add a folder of your own images, click the add button (+) below the list of folders, then choose the folder that contains your images.
For best results, choose images that are stored on your startup disc. Images stored on a different disc may not load reliably after restarting your Mac, depending on how quickly the other disc becomes available after startup.
We hope this helps get you pointed in the right direction.
Take care.
