She politely declined the invitation to avoid hurting their feelings.

politely 是形容词 polite（礼貌的）加上后缀 -ly 构成的副词形式，表示"以礼貌的方式"。polite 来自拉丁语 politus，原意是"打磨光滑的"，引申为"有教养的、文雅的"。