[thstone]

That sound is caused by the starter. What you hear is the teeth of the starter pinion gear grinding on the teeth of the flywheel ring gear.
This happens when the starter pinion gear remains engaged with the flywheel instead of retracting as it should.

If this condition is allowed to continue long enough, the teeth on the ring gear can wear down to the point where the starter will no longer fully engage the ring gear and the starter will simply spin. This can be worked around by pushing the car in gear to move the ring gear to a position where the teeth will engage and then the car will start.

Take the rebuild starter back to whomever worked on it and have it repaired (again) or simply buy a replacement starter.