Supporting Veteran Caregivers Act of 2019 This bill requires the Department of Veterans Affairs (VA) to reevaluate the cases of family caregivers who were removed from the VA family caregivers program or had benefits reduced under such program to ensure the removal or reduction was consistent with the program's eligibility criteria. On the basis of the reevaluation, the VA must (1) offer reinstatement in the program to family caregivers who were improperly removed, and (2) reverse any reduction in benefits that was found to be improper. The VA must compensate family caregivers who were reinstated in an amount equal to the amount the caregivers would have received during the period of removal. Additionally, the VA must compensate family caregivers whose benefits were restored for the benefits they would have received if their benefits had not been reduced.