Think there might be a mix-up here, catholicism isn’t actually growing in China in any significant way. It’s Evangelical Christianity, like in South Korea, that has seen some growth, especially in rural areas and among parts of the emerging middle class.
Catholicism remains quite marginal and is tightly controlled by the state through the Patriotic Catholic Association. So framing it as a potential tool of U.S. influence may be a bit of a stretch. If there’s any real concern for the Chinese authorities, it’s more likely directed toward Evangelical movements with transnational links.
