What is indicated by excessive back and forth movement of the differential?

Excessive back and forth movement of the differential can result from incorrect backlash adjustments in the gear set. Backlash refers to the slight gap or play between the gear teeth when they are not perfectly engaged. If this backlash is out of specification, it may lead to excessive movement as the gears shift during operation. In a properly functioning differential, the amount of backlash must be carefully calibrated to ensure smooth operation and longevity of the gears.

While other conditions can cause issues in the differential, when specifically noting back and forth movement, an incorrect backlash is the most relevant reason among the listed choices. Loss of lubrication can lead to gear wear or overheating, and worn gears can result in noise or grinding but are not primarily associated with excessive movement. Additionally, a damaged case may impact differential performance but typically wouldn't manifest as just excessive movement. Therefore, the relationship between incorrect backlash and excessive movement firmly supports why this choice is the correct response to the question.