No matter whether the warning seems justified at first glance or not: the ostrich tactic of "burying your head in the sand" or sitting it out will not help in any case. The rights holder has decided to pursue the case with a lawyer and has instructed him to enforce his interests. If you do not respond, the lawyer will at best send you another out-of-court letter and - if you still do not respond - pursue the matter in court.
Depending on the facts of the case, the rights holder may even enforce the injunctive relief by means of an interim injunction. However, rights holders are usually primarily concerned with enforcing claims for damages. In this respect too, however, legal action must be expected, even if not immediately. In any case, legal proceedings make the matter even more expensive - often completely unnecessarily.