If the area of the girdling goes completely around the  limb and there is still foreign material in the area, the upper part of the branch is likely to decline or die back over time. Was that limb fully leaved out with normal sized leaves and did it put on new growth? You could just monitor it to make your decision but that area is likely to continue to be a weak point. Do you know what kind of Magnolia it is? Some, like our native Sweetbay Magnolia (https://plants.ces.ncsu.edu/plants/magnolia-virginiana/) tends to grow in a more shrubby, multi-stemmed habit than some other Magnolias.

It also looks like you could, as you noted, prune out the damaged limb, which would encourage the side limb to take over as the main leader. It would grow and straighten over time.

Christine