Large language models (LLMs) have demonstrated promising capability in generating reward functions for deep reinforcement learning (DRL)-based building energy management. However, their potential to exhibit or exacerbate disparities in occupant comfort across heterogeneous demographic populations remains unexplored. We present OccuReward, a framework investigating how LLM-mediated reward design affects demographic equity. Our contribution is three-fold: the introduction of the Comfort Equity Index (CEI) as a novel feedback signal; a methodology for iterative, equity-aware LLM reward shaping; and a performance analysis of DRL agents under these refined objectives. Utilizing four empirically grounded occupant profiles from the ASHRAE Global Thermal Comfort Database II (13,440 votes), we deploy a Soft Actor-Critic agent in CityLearn v2. Our approach employs the Gemini API to generate reward function logic and weights--rather than performing per-step inference--across three refinement rounds. Results across 15 experimental runs reveal that elderly female occupants consistently experience the lowest satisfaction in initial rounds. By Round 3, equity-aware LLM refinement activates specific reward components that improve satisfaction for Young Males (+17.6%), Mid-aged Females (+28.2%), Health Sensitive (+53.8%), and Elderly Females (+567%), while simultaneously reducing energy costs by 3.2%. Our findings highlight that while reward-level intervention significantly improves equity, demographic disparities in AI-driven controllers persist, necessitating further research into algorithmic fairness in building systems.