Which is "visiting central Europe" modifying, "they" or "respite" ?

“As they enjoyed the peaceful respite visiting central Europe, people drank Pilsner beer in cafés and manufactured handsome light machine guns.”

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Wow, I first thought so, but a translator translated it as the other way, so I was wondering.
Thanks a lot.

It was like this. In line 3-4 is that sentence.

Janacek composed his little symphony in 1926. He originally wrote the opening as a fanfare for a gymnastics festival. Aomame imagined 1926 Czechoslovakia: The First World War had ended, and the country was freed from the long rule of the Hapsburg Dynasty. As they enjoyed the peaceful respite visiting central Europe, people drank Pilsner beer in cafés and manufactured handsome light machine guns. Two years earlier, in utter obscurity, Franz Kafka had left the world behind. Soon Hitler would come out of nowhere and gobble up this beautiful little country in the blink of an eye, but at the time no one knew what hardships lay in store for them. This may be the most important proposition revealed by history: "At the time, no one knew what was coming." Listening to Janáˇcek's music, Aomame imagined the carefree winds sweeping across the plains of Bohemia and thought about the vicissitudes of history.

Not at all. Anyway, I'm really glad that I got to realize that you can take the sentence either way, at least in terms of the grammatical structure. Thanks a lot.