As no suitable answer was given, except for a comment by @Shoeless recommending
using AutoHotKey to survey eternally all dialog windows for this one and uncheck
the option (not recommended for such a small problem), I detail below my own
The Photo Gallery is contained in the executable WLXPhotoGallery.exe.
I used Resource Hacker to view its resources, but did not find this
dialog or window as a resource.
The conclusion is that it's generated by the program at runtime,
so cannot be modified except by hacking the program's code.
I used Process Monitor to capture all registry activity of the program,
but have not identified any easily identified related setting.
So it does not look as if this option is controlled by a registry item.
The conclusion is that there is no way to uncheck that checkbox
programmatically, except by using a big canon such as AutoHotKey.
If using AutoHotKey is not an option, you will need to use another viewer.
See the article Best Free Digital Image Viewer
for better and more sophisticated image viewers/browsers
than Microsoft's Photo Gallery.