What I meant was, "Is there any historical grievances between China and Turkey?"
To answer your question, I just spent some time reading up on this actually. Here's what I found:
China does have a grievance dating back to Ottoman/Qing times when the Turks made a half-hearted effort to subvert Chinese authority in Xinjiang. During Yakub Beg's decade-long conquest of Kashgar and its environs, he solicited political and military support from the Ottomans, who agreed to send him weapons, 3000 rifles and some old (actually unusable) cannons, along with a few military officers to train his troops. The Ottomans also granted him the title of emir which theoretically made them overlords of Yakub Beg and Kashgaria. However, everyone knew the Ottomans were too far away to be of actual help, both were actually hoping the British would get involved as a hedge against Russia. In the end, Yakub Beg's army was put down by Chinese forces under the Qing general Zuo Zongtang. Official Ottoman involvement then ceased, although some indirect Turkish influence remained.
After the fall of the Qing, weak Republican Chinese control of the region allowed Turkish influence to increase to a degree. Turkish trained teachers arrived and began setting up schools and teaching a modern Turkish curriculum in Turkish to the Uyghurs. Ironically, this clashed with the conservative clergy and feelings of Uyghur identity and caused some problems. In any case, Turkish influence again receded when the Ottoman Empire fell after WWI.
More recent developments include the fact that Communist China and Turkey were opposing combatants in the Korean War. Turkey also became the base of many Uyghur operations to subvert Chinese control in Xinjiang. On the other hand, China also supported Turkish rivals such as Syria, which annoyed Turkey. Sino-Turkic relations often followed the course of Sino-American relations, they improved after the 1970's with the thaw between China and the United States.
EDIT: Also remember that Turkey delayed the Varyag from passing through the Bosphorus.