Recent literature highlights the potential of graph-based approaches within large language model (LLM) retrieval-augmented generation (RAG) pipelines for answering queries of varying complexity, particularly those that fall outside the LLM's prior knowledge. However, LLMs are prone to hallucination and often face technical limitations in handling contexts large enough to ground complex queries effectively. To address these challenges, we propose a novel iterative, feedback-driven GraphRAG architecture that leverages response quality assessment to iteratively refine outputs until a sound, well-grounded response is produced. Evaluating our approach with queries from the HotPotQA dataset, we demonstrate that this iterative RAG strategy yields responses with higher semantic quality and improved relevance compared to a single-shot baseline.