Why would they do this? They have been getting along with Mongolia pretty well in recent decades.
https://en.wikipedia.org/wiki/China–Mongolia_relations#Modern_period Why attack a friendly neighbor and member of the UN and get universally condemned for it (and remember that China was trying to improve relations with Russia, Japan and the West in the 1990s--and of course to join the WTO)? Also, why add to China's ethnic minority problem? This is not like Taiwan, which is overwhelmingly Han in population and which calls itself the Republic of China, and whose permanent loss is obviously very difficult for the PRC to tolerate.
Bad relations between the PRC and Mongolia during the period of the Soviet-Chinese quarrel were caused not by Chinese irredentism but by China's perception of Mongolia as a Soviet satellite (in particular the presence of Soviet troops there was listed in the 1980s as one of the "three obstacles" to Soviet-Chinese rapprohement[1]). That problem had simply ceased to exist by the 1990s and the Chinese were anxious to improve their political and economic ties with Ulaanbaatar.
[1] The other two were the presence of Soviet troops in Aghanistan and of Vietnamese troops in Cambodia.