Hello Dave, and thank you for writing. Please accept my condolences on your father's passing. Because you did not indicate that your home is underwater (worth less than the mortgage balance), or that you don't want to keep it, I will answer on the assumption that you want to keep the home.
The one thing that I am unsure about is the program your father's mortgage falls under. HARP was a refinance program that allowed homeowners with little equity, no equity or even negative equity to refinance to new mortgages with better terms than the ones they had. It was technically a refinance, not a modification.
If you have a HARP mortgage, it's just a regular mortgage. The law prevents mortgage lenders from forcing heirs to repay mortgages immediately, so you can't be forced out or forced to refinance by the lender as long as the payments are being made.
In 2014, the Consumer Financial Protection Bureau (CFPB) enacted regulations that generally allow heirs to be added to the mortgage. So if you like the terms of the mortgage on the property, contact the loan servicer (the company you make the monthly payments to). The servicer may be a different company than the lender -- servicers process mortgage payments and deal with borrowers after the loan closes. Let them know about your inheritance and they should help you with the paperwork.
However, this is a good time to compare the terms of your HARP loan to that of mortgages available now. Your HARP loan may have a great rate, or a not-so-great rate -- during the program, rates varied from about 3.5 percent to about 5.5 percent. You may be able to save by refinancing. Compare the interest rate and terms you have now to what's available today by checking out today's mortgage rates. https://themortgagereports.com/today
On the other hand, if you have a HAMP (modification) mortgage, check your paperwork. Some have terms that are not permanent. For example, they may include interest rate "step ups" that provide a low rate for a specified time (say, 5 years) and then gradual increases after that (for example, 1 percent per year).
If your home has a HAMP modification, check your terms carefully, because you may want to refinance out of that if it contains interest rate increases beyond rates that are currently available. If your credit rating is better than your father's was, or if your home has more equity now, or if interest rates are better than they were at the time of the modification, you may be eligible for a better deal.
You won't know unless you check.
Thank you for your question, and please write back if you'd like more information.