I got $500 in HEERF (CARES) relief as a student at the University of Utah. Do I need to put this on my tax return?

No.

From page 2 of pub 970:"What's New for 2020 Emergency Financial Aid Grants under the CARES Act. Emergency financial aid grants under the CARES Act for unexpected expenses, unmet financial need, or expenses related to the disruption of campus operations on account of the COVID-19 pandemic, are not includible in your gross income. Because the grant is not includible in your gross income, you cannot claim any deduction or credit for expenses paid with the grant including the tuition and fees deduction, the American opportunity credit, or the lifetime learning credit. See FAQs: Higher Education Emergency Relief Fund and Emergency Financial Aid Grants under the CARES Act."

HEERF student grants are not taxable and do not need to be reported on your tax return.