Depending on your inclinations, you could dig into that disk to find out what files are on it that make Windows think it is a system disc. It's probably fairly obvious, but it could be hidden files or even a partition of some type.
Or just cut your losses and move on to Macrium, Acronis, or EaseUS TODO. That's what many of us on this forum have done. Maybe Microsoft will engineer Windows Backup a bit differently in future releases, but it is a bit touchy, non-intuitive, and inflexible as it now stands.