Recommenders are significantly shaping online information consumption. While effective at personalizing content, these systems increasingly face criticism for propagating irrelevant, unwanted, and even harmful recommendations. Such content degrades user satisfaction and contributes to significant societal issues, including misinformation, radicalization, and erosion of user trust. Although platforms offer mechanisms to mitigate exposure to undesired content, these mechanisms are often insufficiently effective and slow to adapt to users' feedback. This paper introduces an intuitive, model-agnostic, and distribution-free method that uses conformal risk control to provably bound unwanted content in personalized recommendations by leveraging simple binary feedback on items. We also address a limitation of traditional conformal risk control approaches, i.e., the fact that the recommender can provide a smaller set of recommended items, by leveraging implicit feedback on consumed items to expand the recommendation set while ensuring robust risk mitigation. Our experimental evaluation on data coming from a popular online video-sharing platform demonstrates that our approach ensures an effective and controllable reduction of unwanted recommendations with minimal effort. The source code is available here: https://github.com/geektoni/mitigating-harm-recsys.