She picked at the salad daintily with her fork, careful not to stain her dress.

daintily 是形容词 dainty 的副词形式。dainty 意思是"精致的、优雅的"，加上后缀 -ly 变成副词后表示"优雅地、小心翼翼地"。这里形容用餐时动作优雅谨慎的样子。