Veteran Caregiver Application and Appeals Reform Act of 2023 or the CARE Act of 2023 This bill modifies the administration of the Program of Comprehensive Assistance for Family Caregivers under the Department of Veterans Affairs (VA). First, the bill provides that relevant medical specialists must be part of the application review process for veterans and their family members applying to participate in the program. Under current law, the VA must provide notifications regarding decisions affecting the furnishing of assistance to individuals who submit applications for the program and their family caregivers. The bill requires that the VA provide such notifications to individuals who are being reassessed for eligibility to continue in the program. Additionally, the bill requires that such notifications include all criteria used to determine eligibility for assistance and how the criteria were used to evaluate information provided in assessments to determine eligibility. The bill also requires the VA to report annually on the program. Finally, the bill requires the VA to establish a process through which it may recognize organizations and individuals to assist veterans, their family members, or caregivers, in navigating the programs and services of the Veterans Health Administration. The VA must solicit feedback and recommendations from relevant organizations in the creation of such a process. In order to be recognized under the established process, individuals and organizations must certify that no fee or compensation will be charged to individuals for the provision of assistance.