Hola Emanuel,
"Por entonces" refers to "at that time","around that time", "then", "back then"; with this same meaning we also use "por aquel entonces", or"en aquel entonces.
However "Para entonces" refers to "by then", indicating more precisely "up to then" similarly to when we use it as a dead line, e.g. "Quiero el informe para mañana.", or "Voy a hacer la compra y volveré en 30 minutos. Para entonces tienes que haber terminado los deberes.".
I've changed the translation in the lesson to be more precise.
Gracias y saludos.
Inma
