Actually some of the answer is found on Wikipedia, but in the [pan-Mongolism article](https://en.wikipedia.org/wiki/Pan-Mongolism):

> In 1943, the British Foreign and Commonwealth Office predicted that the Soviet Union would promote the idea of a Greater Mongolia to detach China's Inner Mongolia and East Mongolia from Chinese influence.[46] A year later, the then-Soviet satellite Tuvan People's Republic was annexed by into the Russian SFSR. During the Soviet invasion of Manchuria in August 1945, Outer Mongolian troops occupied both Inner and Eastern Mongolia, and Japanese collaboratist leaders like De Wang were kidnapped to Outer Mongolia to be inculcated with pan-Mongolist ideals. **Perceiving an imminent threat to China's territorial integrity, Chiang Kai-shek signed an agreement with the Soviets during the Mongolian occupation which gave Chinese recognition of Outer Mongolian independence. In return for the fulfillment of this longtime Soviet foreign policy goal, the agreement stated that Mongolian independence would only be effective "within [Outer Mongolia's] existing frontiers". The Outer Mongolian troops subsequently withdrew from China.**[42] In 1947, Chiang renewed his claim on Outer Mongolia in response to alleged Mongolian incursions into Chinese Xinjiang during the Pei-ta-shan Incident.[39]

So there was a (little known, perhaps) deal between Chiang Kai-shek and the Soviets which exchanged Chinese (ROC) recognition of (Outer) Mongolia seemingly in return for the latter dropping any further territorial ambitions in [the rest of] China. Although Chiang Kai-shek did consider the deal void a couple of years later, there was apparently no substantial Soviet/Mongol retaliation before the PRC/Mao came to power. It's not clear just from that snippet if this lack of post-1947 Soviet/Mongol retaliation was because of time constraints or other considerations.

Frankly Wikipedia has a very confusing article on the [Pei-ta-shan Incident](https://en.wikipedia.org/wiki/Battle_of_Baitag_Bogd) aka the battle of Baitag Bogd; sporadic fighting seems to have lasted for a year (into 1948), so it's possible I'm missing something. But what seems rather certain is that Stalin apparently did not wish to broaden that conflict.