It is theoretically possible for fact-checkers to be sued for libel and defamation, but this has not yet happened.
In one recent example, the former TV journalist John Stossel filed a lawsuit against Meta, arguing that the respective labeling of two of his videos as "misleading" and "missing context" constituted defamation. Stossel's lawsuit was dismissed because he could not prove that Meta acted maliciously. Nor was his argument that the fact check on one of his videos misquoted him sufficient grounds for a defamation claim, because fact-checkers do not need to be responding to a verbatim statement made by the individual or article being fact checked.
Suppose someone shares a post (or article, or video) on Facebook which implies a claim but does not outright state it, or misrepresents relevant facts by failing to provide necessary context. In that case, fact-checkers will label that post with the appropriate tag. For instance, in one of the videos that Stossel claims were wrongfully fact checked, he accurately discusses the effect of 20th-century fire suppression policies and the resulting buildup of vegetation on the landscape. However, the video also dismisses the impact of climate change on the environment, which is not a position supported by contemporary climate science research. For this reason, his video was labeled "missing context."
While it remains possible for fact-checkers to be targeted in lawsuits, there have not yet been notable successful cases where this has happened, because the labels applied to posts that get fact checked are legally considered "protected opinion." The determinations given by Meta's third-party fact-checkers cannot constitute defamation unless no grounds are provided for the labels applied to the post. This means that fact-checkers have to provide evidence or citations from reliable and reputable sources.
It is true that fact-checkers can be sued if there is a case to do so.