"Allowable Rescission"

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A borrower would like to refinance two $(2)$ loans, her primary residence in town and her lake house. Though the payments have been made on time for both properties, a decrease in the borrower's income, along with a higher standard for underwriting approval, has made the borrower ineligible for the requested mortgage on the lakefront property. In order to refinance the second home the mortgage loan originator advised the borrower that a cosigner would be needed. The borrower discussed the situation with her parents, and they agreed to cosign for the mortgage loan, and the closing went as planned.

After the closing, the parents had second thoughts about their obligations. They realized that if anything happened to their daughter's finances, they would be obligated to make those payments, which would be very difficult for them financially.

The parents told their daughter that they were rescinding the refinance and wanted her to pursue other avenues of financing.

Is this a process that the parents are allowed to pursue?