Okay, I'll bite.
The first major operation the Romanian forces had a hand in after crossing the Dniester was Uman, where 100.000 Soviets were killed or captured. Romanian divisions secured the flanks of the Hungarian corps that was one of the pincers, and the helped clear out the pocket. Without them, some of those Soviets escape, and taking out the rest takes longer. Potential impact down the line at Kiev.
Next we have the Siege of Odessa. Here there is suddenly no one available to assault the city, hence why I think the Germans will have to resign themselves to simply screening it with whatever they can find that's uncommitted elsewhere - Slovaks, crappy Hungarian infantry divisions, Italians, all interspersed with the odd German battalion here and there. They will not have the numbers nor the equipment to assault the city, meaning it will likely hold out far longer than anyone would otherwise expect, even more so since the Romanian Navy and Air Force won't be around to limit resupply attempts by sea. Without the losses the defenders suffered OTL from the continued attacks, it's doubtful STAVKA orders an evacuation anytime soon.
Next we have the battle of Kiev, where Romanian forces were vital in manning German flanks as they crossed the Dnepr. Without them, it will take more time to bring up other units to support the attack, and it may bog down the panzer groups longer than expected and/or require heavier fighting (and thus increased losses from combat and attrition). Taking into account a different Uman pocket (see above), and Guderian's panzers may not even be in a position to take part in Typhoon, or, if they do, they may not get as far, possibly even failing to properly clear the Vyazma pocket - and that's potentially hundreds of thousands of Soviet soldiers having a chance to break out.
Where things really get dicey for the Germans is further south though. Here, the Romanians were instrumental in holding the line whilst the assault on the Perekop Isthmus (to break into the Crimea) took place. Without them, there probably isn't any attack on Crimea at all in '41. On the flip side, von Runstedt might not stick his neck out all the way to Rostov come winter. Thus, any attack on Crimea is likely to come as a prelude to Case Blue in '42, athough by then the Soviets would have had many months in which to fortify that narrow strip of land, in which case Hitler might chose to ignore Crimea all together and just push east, leaving a screening force behind like at Odessa.
As to how Case Blue itself might go, i don't have the wildest clue. the losses suffered by the Soviets in their failed bid to rescue Sevastopol (
170.000 men) are butterflied away, whilst the Axis has a lot less to work with. With what units they man those flanks I have absolutely no idea.