It looks to me like all your images are either in the /assets/images directory, or the images/ directory. You can see the location by hovering over an image in your browser, right-clicking on the image, selecting "Copy image location", then going to a text editor and pasting the location (that's how I got the image link below).
http://swamph2o.com/assets/images/kids-swimming.jpg
I suspect that the site is old enough that those are the real locations. Lucky for you, the images have meaningful names.
I'm guessing here, but I think if you go to Resources -> Manage Files and click to expand the images and assets/images folders, you may see your image files. If that version of MODX has an upload option in the Files section, you may be able to upload new versions of the files right there.
If not, go into cPanel's File Manager, look under the public_html folder for the images and assets/images folders. If you find your image files there, you can upload new ones using the upload button at the top of the File Manager screen.