"They couldn't travel when they were young."
Translation:Ils ne pouvaient pas voyager quand ils étaient jeunes.
"Ils n'ont pas pu" would refer to a particular event in time. It would suggest that they suddenly became unable to travel, or they were unable to travel on a specific occasion. The imparfait is a better translation for "couldn't."
Note that, even if it were correct to use the passé composé here, your word order is not quite right -- it would be "ils n'ont pas pu."
It seems odd to refer to 'use to' in both clauses. The phrase does not say why they could n't travel only when they could not travel, i.e. when they were young. I believe that the translation provided should have been along the lines of, stating that when they were young 'ils etaient', followed by clear statement ' ils ne peuvent pas voyager'. It is all down to assumptions.