If this is about csl.mendeley.com links to custom styles, you'd have to ask Mendeley, we don't know how those work and have no control over them.

For style on editor.citationstyles.org, they're only stored locally in your browser, so clearing cookies is all that'd take.

It was about the csl.mendeley.com links to custom styles. Clearing cookies does not delete custom styles. It is also not obvious where these custom styles are stored in https://csl.mendeley.com/. The first custom style adds the "First Second" name to the style, and subsequent styles add -2.

I'm afraid you'll need to ask Mendeley; they're stored on their server somehow