If you click on the Parsoid user notice it dismisses (and stays dismissed for a week or more) but this is not very discoverable.
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Note that the message can be changed on-wiki (without requiring a code change) by editing [[MediaWiki:ParserMigration-notice]]` as documented in the README at https://gerrit.wikimedia.org/g/mediawiki/extensions/ParserMigration so this can be prototyped on-wiki and then the final message backported to code as the default message for all wikis.
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I filed T358296: [UX] No obvious way to close notice dialog telling me that I'm using the Parsoid view experimental feature, but I think that my complaint is really more about the UX mw.notification in general than your particular usage of it.