The HMDA definition of a refi is: (p. 29 Getting it Right)
Any dwelling secured loan that replaces and satisfies another dwelling secured loan to the same borrower. The purpose of the loan being refinanced is not relevant to determining whether the new loan is a refinancing for HMDA purposes. Nor is the borrowers intended use of any additional cash borrowed relevant to determining whether the loan is a refinancing, though the borrowers intended use of the funds could make the transaction a home improvement loan or a home purchase loan.
Therefore, from what you’ve mentioned already, I’d classify this loan as a refinance and on the LAR I’d call it a purchase.
IF the parents did not have a previous mortgage you could consider this to be, in essence an Equity loan. Usually these are not reportable to HMDA, depending on what the proceeds were used for.
Hope this helps! 😀