The modern approach would treat the offer as irrevocable. To motivate this approach, add some facts to the case. Suppose that, to pay off the mortgage early at a reduced amount, Petterson had to spend considerable time and effort raising the necessary cash.
Imagine Pattberg knew this and that he intended his offer to be an inducement to expend the time and effort necessary to raise the cash. Imagine Pattberg made the offer because he needed money and saw no other way to get except to induce Petterson to pay off the mortgage early.
After making the offer, Pattberg had the chance to sell the mortgage to another person (for a reduced amount), and he did so despite knowing that Petterson was, in reliance on the offer, working to raise the cash he needed.
It is arguably unfair to Petterson to induce him to spend the time and effort to raise the cash and then make all that time and effort wasted by selling the mortgage to someone else.