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.
The Korean War severely damaged US relations with Communist China. This is not to say that the US and Red China had good relations prior to the war. However, the relationship had not really been set. Communist China had only existed for about a year when the Korean War started.
But the Korean War ensured that the relationship would be a bad one. This is because the US and the Chinese ended up directly engaged in combat with one another. Once this happened, there was no hope for a good relationship. The US did not have any sort of relationship with the Mainland until the 1970s.
The Korean War was fought from 25th June, 1950 to 27th July, 1953. It resulted in North Korea becoming Communist and South Korea becoming non-Communist. China provided aid to North Korea during this war and consequently this resulted in tensions between U.S.A. and China. Initially the Communists were very successful and conquered most of South Korea, but this situation was dramatically reversed when General Douglas Mac Arthur led his troops victoriously almost to the Chinese border on the North of the Korean peninsula.The Korean War was the only time that U.S. troops fought directly with the Red Army of China. The Korean War established that the U.S.A. was ready to intervene with military force to check the spread of Communism.
The Korean War was between the North and the South. America became the South's ally while Communist China was the North's ally. As a result, America and Communist China had troops fighting against each other in the Korean War. The Korean War did some damage and hurt the relationship between America and Communist China because their troops fought against each other as well as political differences. Communist China supported the North Korean dream of conquering the South and the whole communist vision and taking control of people. On the other side was America who supported the South's vision of freedom and not becoming a communist nation. The political differences also severed the relations between China and the United States. But there was never a war between China and the United States directly. It was just during this Korean War that there were troops from these two countries fighting against each other.