Instead they had to suck it up and march East into Russia proper.
Romanian troops took part, willingly, of Nazi death squad actions.
Furthermore, Jews in Romania didn't remember the Germans "fondly".
Simply put: there's a huge difference between being outright conquered, occupied, and subject to the control of a puppet regime (like Poland, Ukraine, Greece), and the local regime proactively deciding to form an alliance (as did the governments of Hungary, Finland, and Romania). Even if that decision was made under a considerable degree of duress.
That's just the basic storyline of the war. And it's all I have time for. But trust me, just take another look at the basic event chronology and you'll easily see why.
You wrote your initial comment stating a patent falsehood: that Romania was "basically under German occupation". It was under nothing of the sort. Their fascist dictatorship eagerly helped the Germans and it's officially considered part of the Axis (just not one of the major three powers).
> (like for example what you wrote about the Einsatzngruppen troops)
Romanian troops participated in the Odessa massacre and, as one of the Axis nations other than Germany most involved on the Eastern Front, participated in Einsatzkommando actions.
And the point still stands: Romanian Jews certainly don't remember the Germans "fondly".
Romania was an Axis ally under a fascist dictator, Antonescu, and was not under German occupation. Why would Germans steal or loot from a willing ally? Romanian troops participated with around 280,000 to 380,000 Jewish deaths to the Holocaust. I suppose Jews in Romania don't remember their German "allies" too fondly.
> The subsequent occupation by the Russian Red Army music less so…
The Soviet (not Russian) Red Army was indeed brutal with former Axis allies. It shouldn't come as a surprise that siding with Nazi Germany was retroactively a terrible choice.