There is a rapidly-growing research interest in engaging users with multi-modal data for accurate user modeling on recommender systems. Existing multimedia recommenders have achieved substantial improvements by incorporating various modalities and devising delicate modules. However, when users decide to interact with items, most of them do not fully read the content of all modalities. We refer to modalities that directly cause users' behaviors as point-of-interests, which are important aspects to capture users' interests. In contrast, modalities that do not cause users' behaviors are potential noises and might mislead the learning of a recommendation model. Not surprisingly, little research in the literature has been devoted to denoising such potential noises due to the inaccessibility of users' explicit feedback on their point-of-interests. To bridge the gap, we propose a weakly-supervised framework based on contrastive learning for denoising multi-modal recommenders (dubbed Demure). In a weakly-supervised manner, Demure circumvents the requirement of users' explicit feedback and identifies the noises by analyzing the modalities of all interacted items from a given user.