Preventive Care Awareness Act of 2022 This bill requires activities to promote the use of preventive health care services with a particular focus on decreasing disparities in accessing preventive services for individuals in rural and underserved communities who delayed or forewent recommended preventive services during the COVID-19 pandemic. Specifically, the Department of Health and Human Services (HHS) must carry out a campaign to increase public awareness about and use of recommended preventive services. HHS must also convene a task force to develop recommendations regarding preventive services during and after the COVID-19 pandemic and future pandemics. The recommendations must address, among other considerations, reducing disparities in health outcomes and identifying barriers to implementing the recommendations. Additionally, the bill allows states, Indian tribes, and territories to use a portion of their Preventive Health and Health Services Block Grant funding for FY2023 and FY2024 on activities to increase patient uptake of recommended preventive services.