Q. Is there a tax penalty if I just hold on to that refund?
A. Yes.
You have 60 days, from the date of the refund, to put the money ("re-contribute") back into the 529 plan, to avoid that part of the original distribution being considered "non qualified". "Non qualified distributions are subject to tax plus a 10% penalty on the earnings portion of the distribution.
For 2020, the IRS has issued temporary guidance to extend the usual 60 day redeposit window so that you may return tuition refunds to the 529 plan by July 15, 2020 in order to avoid a situation where the funds create taxable income. When returning contributions to the plan sponsor, be sure to indicate that the funds are a recontribution by including a letter of instruction or other notation with the funds.
See a similar question at https://ttlc.intuit.com/community/college-education/discussion/re-refund-of-qualified-expense-repaym...
