Collaborative-filtering (CF) scores provide graded, personalized rewards for training large language model (LLM) recommenders through reinforcement learning. However, these rewards can cause exposure collapse: even though the CF model itself produces diverse top recommendations across users, an LLM optimized with its rewards concentrates on fewer items. We decompose each score into an item-mean component, the item's average CF score across user histories, and a residual component, the current user's score deviation from the average. Through controlled interventions, we identify the item-mean component as a contributor to exposure collapse. Accordingly, we propose two reward corrections: per-item centering removes each item's estimated mean score, while per-item standardization further rescales the residual using its estimated standard deviation. Experiments on two datasets with two identifier schemes show that both corrections substantially improve catalog coverage and exposure evenness. Compared with training on the uncorrected CF reward, our corrections increase the number of distinct items ranked first across users by up to $9.8\times$, while maintaining comparable ranking accuracy. Code is available at https://anonymous.4open.science/r/LLM4Rec-CF-Bias-27EF/.

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