Despite growing interest in using LLMs to generate feedback on students' writing, little is known about how students respond to AI-mediated versus human-provided feedback. We address this gap through a randomized controlled trial in a large introductory economics course (N=354), where we introduce and deploy FeedbackWriter - a system that generates AI suggestions to teaching assistants (TAs) while they provide feedback on students' knowledge-intensive essays. TAs have the full capacity to adopt, edit, or dismiss the suggestions. Students were randomly assigned to receive either handwritten feedback from TAs (baseline) or AI-mediated feedback where TAs received suggestions from FeedbackWriter. Students revise their drafts based on the feedback, which is further graded. In total, 1,366 essays were graded using the system. We found that students receiving AI-mediated feedback produced significantly higher-quality revisions, with gains increasing as TAs adopted more AI suggestions. TAs found the AI suggestions useful for spotting gaps and clarifying rubrics.

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