To rebuff something, such as an offer or suggestion, is to reject or criticize it sharply. One can also rebuff a person by rudely rejecting or refusing them.

// When their request was immediately rebuffed by upper management, the staff was left frustrated yet also more determined.

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“The state rebuffed the lawyers’ efforts to use the fees as seed money for a new technology system.” — Robert T. Garrett, The Dallas (Texas) Morning News, 15 Feb. 2023

Many English verbs begin with the prefix re-, meaning “again” or “backward,” so we wouldn’t criticize you for drawing a connection between rebuff and buff, a verb meaning “to polish or shine.” But rebuff would beg to differ: this word comes to us from the Middle French verb rebuffer, which traces back to the Old Italian ribuffare, meaning “to reprimand.” (Buff, in contrast, comes from the Middle French noun buffle, meaning “wild ox”). A similar word, rebuke, shares the “criticize” sense of rebuff, but not the “reject” sense; one can rebuke another’s actions or policies, but one does not rebuke the advances of another, for example. Like rebuke, rebuff can also be used as a noun, as in “The proposal was met with a stern rebuff from the Board of Trustees.”