I have received a cease-and-desist letter (Abmahnung)

The heart of the matter

1. Three demands, three checks. Injunctive relief (Unterlassung), damages and warning costs are different things with different requirements. A demand to stop can be made even without fault. Damages require intent or negligence; the costs require a justified warning letter and, in copyright and competition law, the legally required information as well.
2. The signature binds you permanently; payment is a separate point. A cease-and-desist declaration (Unterlassungserklärung) usually applies for life; any later breach can trigger the contractual penalty. Giving it does not automatically mean you have to pay every amount demanded. A modified version can be worded without any promise to pay.
3. The deadline is serious, but it is not a statutory deadline. The deadline in the warning letter is set by the other side itself, often only a few days. If you ignore it, you risk a preliminary injunction or a lawsuit. An extension can often be agreed, but there is no right to one. It is different with court deadlines, for example after a payment order (Mahnbescheid) or a lawsuit: if you miss them, you risk a default judgment or an enforcement order without the matter being examined.
4. Removing is not an admission. Removing the content complained about ends its further use and is not an admission of the allegations. Secure evidence first. Do not write to the other side about the substance until you have had advice.
5. Private or commercial use decides the costs. For private use in copyright matters, the warning costs are usually capped at an amount in dispute of 1,000 euros, which under the current fee table is around 168 euros including VAT. For commercial use and in trademark law, this cap does not apply. It never covers damages.