On the 13th (local time), the fact sheet for the summit that South Korea and the United States jointly released included wording that revealed the U.S. intent to keep China in check.
According to the White House website, the word "China" did not appear directly in the fact sheet. However, it carried the intent of the Donald Trump administration to have the South Korean military and U.S. Forces Korea play a more active role in checking China.
The most notable example is "strengthening conventional deterrence posture against regional threats." The fact sheet said, "The two countries will strengthen the United States' conventional deterrence posture against all regional threats to the alliance, including North Korea," and the "regional threats" referenced here are effectively interpreted as being aimed at China.
To that end, South Korea "will lead combined conventional defense against North Korea with U.S. support" and "accelerate efforts to strengthen essential military capabilities." While the primary purpose of strengthening South Korea's conventional military capabilities is to respond to threats from North Korea, it can also be seen as intended to check China.
It is also noteworthy that the two sides said they "confirm the relevant understandings since 2006." This refers to the 2006 joint statement between South Korea and the United States, whose main point was that "as an ally, South Korea fully understands the logic of changes in the United States' global military strategy and respects the need for the strategic flexibility of U.S. Forces Korea."
The part where the two sides said they "decided to strengthen trilateral cooperation with Japan" is also seen as reiterating the need for South Korea-U.S.-Japan cooperation to deter not only threats from North Korea but also those from China.
The fact sheet that day also reflected both sides' understanding that they would respond firmly to Chinese provocations in the Yellow Sea and in airspace. It said, "The two leaders reaffirm efforts to uphold freedom of navigation and overflight and other lawful uses of the sea," and "reaffirm that all maritime claims by states must be consistent with the law of the sea."
The cross-strait issue (between China and Taiwan), where the United States and China clash most sharply, was also mentioned. In the fact sheet, South Korea and the United States "emphasized the importance of maintaining peace and stability in the Taiwan Strait. The two leaders encouraged the peaceful resolution of cross-strait issues and opposed unilateral changes to the status quo," which could be a somewhat sensitive point for South Korea.