To withdraw or retract something (e.g., an application, a claim, a lawsuit); to abandon or cancel a previously submitted request.
彼は告訴を取り下げた。
He withdrew the complaint.
雑誌は誤報を認め、問題の記事を取り下げた。
The magazine admitted the error and withdrew the problematic article.
苦情を取り下げるなら和解に応じます。
If you withdraw the complaint, we'll agree to a settlement.