John - this is not sloppy shooting. This is unavoidable with on-camera flash, or even off camera flash that is still close to the optical axis of the lens.
Reflective tape is designed to mirror light back in the direction it has come from. It does so extremely effectively. Even in your underexposed image, it is clearly the brightest object (in fact the whites from the tape are blown out). The only way to correct this is to clone it out. If you look at your image carefully, the blown highlights extend into the girl's hair.
How to avoid it? Don't use on-camera flash.