The integration of large language models (LLMs) into topic modeling has shown promise for improving topic interpretability and coherence, particularly by exploiting the generative capabilities of LLMs through instruction-based prompting. However, existing methods often incur substantial computational cost and inference complexity. To address these limitations, we propose **LLMFeed**, a novel framework that leverages **feed**back from an **LLM** to improve topic model optimization. Specifically, the LLM is used to **evaluate** topic quality, **identify** semantic meaning, and **recommend** representative topic words. These signals are then incorporated to (i) refine topic representations via Direct Preference Optimization (DPO), and (ii) guide contrastive learning for improved document-topic assignments. Extensive experiments show that **LLMFeed** achieves a 7.6% gain in topic coherence and over 10% improvement in doc-topic distributions on 20 Newsgroups dataset, while requiring only minutes to run, compared with hours for recent LLM-integrated topic modeling methods.