FYI, I think the term you're slightly misusing is "running the gauntlet", which means to face a difficult trial, usually in public. Although you may be mixing it up with "to pick up the gauntlet" (but not run with it), which means to accept a challenge.
https://en.wikipedia.org/wiki/Running_the_gauntlet https://www.dictionary.com/browse/throw-down-the-gauntlet