First, understand a little background The Korean War began in June of 1950, while barely a year earlier, in 1949, there was a communist revolution and the government was overthrown in China. Second, This was during the earliest and some of the most tense years of the Cold War. The United States had consistently refused to allow communist China to take a seat on the UN Security Council, claiming it wasn't the legitimate China and vetoing it each time it was proposed. So it's difficult to say that it damaged relations between the US and China, because we didn't have good relations, or really, any relations by the time the Korean War started.
Of course, in December 1950 the US started fighting Chinese troops directly, and then our very poor relationship deteriorated even further.