As I recall, the bar connects just the bottom halves of the rings. It doesn't necessarily limit the scope to a straight tube, but it does limit the choices to older scopes that do not have an adjustment boss that surrounds the tube. Older models only have the boss on the top and right side.

These mounts were not the highest of quality (although they did a fine job). I think cutting the bar off might effect the stability of the top as it sits in the mount. The nice think about these mounts is that it allows you to pivot the scope to the left for loading, expecially if you have a model 1950 M-S that still had the stripper clip guides.