Vision-language models (VLMs) have gained traction as auxiliary reward models to provide more informative reward signals in sparse reward environments. However, our work reveals a critical vulnerability of this method: a small amount of noise in the reward signal can severely degrade agent performance. In challenging environments with sparse rewards, we show that reinforcement learning agents using VLM-based reward models without proper noise handling perform worse than agents relying solely on exploration-driven methods. We hypothesize that false positive rewards -- where the reward model incorrectly assigns rewards to trajectories that do not fulfill the given instruction -- are more detrimental to learning than false negatives. Our analysis confirms this hypothesis, revealing that the widely used cosine similarity metric, when applied to comparing agent trajectories and language instructions, is prone to generating false positive reward signals. To address this, we introduce BiMI (Binary Mutual Information), a novel noise-resilient reward function. Our experiments demonstrate that, BiMI significantly boosts the agent performance, with an average improvement ratio of 44.5\% across diverse environments with learned, non-oracle VLMs, thereby making VLM-based reward models practical for real-world applications.