Knowledge graphs (KGs) provide a structured representation of real-world facts as triples consisting of entities and their relationships. With the rapid progress of large language models (LLMs), recent studies increasingly explore LLMs for end-to-end KG construction from text. In particular, generative knowledge extraction (GKE) builds KGs by directly generating structured triples from documents. However, generation errors are inevitable, and the resulting KGs often contain triples that do not align with the facts expressed in the source text. To address these issues, we propose GraphRefine, a framework that performs triple-level refinement on KGs constructed via GKE. We first analyze factual inconsistencies that arise in GKE and categorize their types based on a human evaluation. We then construct training data reflecting these types and fine-tune an LLM as a KG refiner. Given a draft KG, the fine-tuned refiner selects a refinement operation for each triple and, if needed, deletes, edits, or rewrites it to reduce factual inconsistencies. Extensive experiments demonstrate that GraphRefine goes beyond deletion-only approaches and improves KG quality from diverse perspectives.