https://www.techdirt.com/articles/20210423/14243646669/content-moderation-case-study-google-refuses-to-honor-questionable-requests-removal-defamatory-content-2019.shtml

Summary: Google has long been responsive to court orders demanding the removal of content, if they're justified. Google has fought back against dubious orders originating from "right to be forgotten" demands from outside the US, and has met no small amount of DMCA abuse head on. But, generally speaking, Google will do what's asked if there's a legal basis for the asking.

But not everyone approaching Google acts in good faith. First, there are any number of bad actors hoping to game the system to juice their Google search rankings.