Most mortgage lenders require a loan title policy. The loan policy is tied to one mortgage and doesn't transfer to a new mortgage. So, when you are paying off one mortgage to get another, the new mortgage will get its own loan policy. The old policy dies with the payoff.
There are very few mortgage lenders, if any, who will do a modification. These are lenders who do not sell their mortgages. Yes, it's rare, but there are still some mortgage lenders who loan for their own portfolio. In the case of a modification, the old loan policy can stay in place and a modification endorsement is used to extend coverage to the modified lien. There are costs involved but usually less than a total refinance.
Now, getting back to reality, most borrowers are closing a full refinance, with or without cash back. Talk to more than one title insurance agent to explore discounted rates. Don't rely upon your mortgage lender. They may not understand the available discounts. Shop around.
In Pennsylvania, we have a few levels of reduced premiums depending on the length of time since your last mortgage closed.