Complicated subject. Rabbi Yonah Reiss of the Beth Din of America has lectures on this matter. He noted that a hundred+ years ago in Eastern Europe, the couple would settle everything, square it all away, and then the very final step would be the Gett.
Today in America, common practice is for the Gett to be the very first step after the couple have moved out and decided it is over. Then they can kill each other fighting over the money, kids, or the like. (The concern is if it's left till the end, it may never happen, or be used as leverage.)
If I'm reading this correctly, the issue raised by the Rabbis Feinstein is specifically if the order is: a.) they agree to some settlement. b.) The Gett is given. c.) She reneges on said agreement.
Again, if I'm reading it correctly, the issue here is that it now looks like the whole Gett was under false premises. Suppose first the couple settles (between themselves) that he'd get 50%; then they do a Gett; then she refuses to hand over the keys unless she gets 60%. He could then claim "I only agreed to the Gett with the assumption that I'd get 50%" ... leaving the Gett possibly invalid.
That's kind of a niche case. There are several ways to avoid it, fortunately, as I'd see it:
A.) Don't do the Gett until everything is totally done and squared away.
B.) Do the Gett after a legally-binding arbitration agreement is signed, so no one in their right mind will try to renege on it.
C.) Just don't renege on the settlement! This letter isn't saying "you can't do the Gett at this point"; it's telling the unhappy ex to deal with the terms of the agreement. Once Rav Moshe told such a person to back down from their complaint, the Gett remained valid and everyone went their own way.