Parole is indeed the word that all parties would have used and understood in 1945. In fact, this is a military tradition that has roots going back as far as Roman Empire - for example, Marcus Atilius Regulus was released on parole by the Carthaginians in 250 B.C.. It was relatively common through the end of the American Civil War, where it was done through POW exchanges on the condition that the prisoners exchanged would not return to military service.
I've run across some references to paroles occurring during World War I, but by that time they seem to have been limited to allowing POWs outside of camps during the day and not repatriations. This practice was ended by the French after the Germans failed to allow paroling of French officers. International law at the beginning of World War II recognized POW paroles, and was specifically mentioned in the Hague Convention of 1907, Chapter 2, Articles 10 through 12:
Art. 10. Prisoners of war may be set at liberty on parole if the laws of their
country allow, and, in such cases, they are bound, on their personal
honour, scrupulously to fulfil, both towards their own Government and
the Government by whom they were made prisoners, the engagements they
have contracted. In such cases their own Government is bound neither
to require of nor accept from them any service incompatible with the
Art. 11. A prisoner of war cannot be compelled to accept his liberty
on parole; similarly the hostile Government is not obliged to accede
to the request of the prisoner to be set at liberty on parole.
Art. 12. Prisoners of war liberated on parole and recaptured bearing
arms against the Government to whom they had pledged their honour, or
against the allies of that Government, forfeit their right to be
treated as prisoners of war, and can be brought before the courts.
The way that such arrangements have been policed have mainly been through means similar to article 12 of the Hague Convention. That is, if a combatant is recaptured on the battlefield and found to be in violation of a prior parole they would not be treated as a POW - in many cases this would mean that they would be executed.
Friedrich Petersen is actually the only reference that I can find for a traditional POW parole in World War II. Other instances seem to be confined to neutral countries such as Switzerland, Spain, and Turkey, but these were usually conditional on the parolee not leaving the country and obviously were not between belligerents.
Brown, Marcus, Prisoner of War Parole: Ancient Concept, Modern Utility, Military Law Review Vol. 156