Knowledge graph question answering (KGQA) involves answering natural language questions by leveraging structured information stored in a knowledge graph. Typically, KGQA initially retrieve a targeted subgraph from a large-scale knowledge graph, which serves as the basis for reasoning models to address queries. However, the retrieved subgraph inevitably brings distraction information for knowledge utilization, impeding the model's ability to perform accurate reasoning. To address this issue, we propose a Question-guided Knowledge Graph Re-scoring method (Q-KGR) to eliminate noisy pathways for the input question, thereby focusing specifically on pertinent factual knowledge. Moreover, we introduce Knowformer, a parameter-efficient method for injecting the re-scored knowledge graph into large language models to enhance their ability to perform factual reasoning. Extensive experiments on multiple KGQA benchmarks demonstrate the superiority of our method over existing systems.