FineREX is a domain-specific knowledge graph pipeline that uses a fine-tuned LLM for named entity and relationship extraction. It outperforms general-purpose models by 15.50% in entity F1-score and 31.46% in relationship F1-score, reducing legal noise by nearly half and node duplication from 17.78% to 11.-17%. The system also cuts end-to-end processing time by 50.0% by eliminating redundant steps.