Budget-constrained IoT service composition seeks composite services that optimize Quality of Service (QoS), such as response time, while operating within a fixed budget, which is a challenge of practical importance since real-world IoT systems often face strict financial limits. Traditional constraint-handling techniques, such as penalty methods, and random repair operators, often struggle to effectively balance budget feasibility and response time optimization. To address this gap, we propose Cost-Aware Repair-based Genetic Optimization (CARGO-IoT), which combines priority-based selection of infeasible solutions with a two-stage repair strategy. CARGO-IoT focuses on repairing recent solutions with smaller violations and faster response times, using a replace-based method guided by learned probabilities from past solutions and a reduce-based method that eliminates redundant services to meet budget limits. Experiments demonstrate that our approach significantly outperforms state-of-the-art methods in this field, achieving lower response time while maintaining budget feasibility.