"Peggiore nostalgia" is not "greater regret". It sounds really weird because the translator brought the consequence to the beggining, and he changed "worse" to "greater". The sentence is completely changed and seems to be wrong.
The translation seems to be perfectly right.
Let me explain something.
"Peggiore nostalgia" is understood as "worse longing" right?
You can use "greater" in the same sense as "worse" before a noun which has a negative connotation. In this case: regret, which is a synonym of longing.
See what I mean?
That means: "non c'è peggiore nostalgia" can be translated correctly as: "there is no grater regret" or "there is no worse longing" as well.
I would have liked the last one better, but since the translator chose the first, I can't say it's wrong.