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Essay critiques refer to the textual assessment of an essay, serving as the basis for the scoring of the essay, and are crucial for the improvements of the essay. Essay critique generation has received increasing attention after the blooming of large language models (LLMs), which show promising potential in writing and critiquing essays. Automatic critique generation can streamline both instructors and reviewers as well as spur LLM advancement in long context generation characterized by essay writing. However, current LLMs suffer from hallucinations when generating essay critiques, which are still under-explored in the community. To facilitate research in reliable essay critique generation, we first define this task with a unified input-output format as well as clear judging criteria. To minimize hallucinations in critique generation, we introduce RedHat, a novel approach that embeds the key information from essays directly into the generation process through document-level question-answering, ensuring critiques stay firmly anchored to the original text. We collected a large-scale, high-quality essay critique dataset called EssayC, annotated by human experts over multiple LLM-generated critiques, from a campus undergraduate essay writing course. We experimented RedHat backboned by commercial and open-sourced LLMs. Results showed that critiques generated by RedHat are preferred by human experts over baseline in 20% of cases on EssayC in detailedness and informativeness, with a decrement around 10% on hallucinations in our judging criteria.