In the context of English as a Foreign Language (EFL) writing education, LLM-as-a-tutor can assist students by providing real-time feedback on their essays. However, challenges arise in assessing LLM-as-a-tutor due to differing standards between educational and general use cases. To bridge this gap, we integrate pedagogical principles to assess student-LLM interaction. First, we explore how LLMs can function as English tutors, providing effective essay feedback tailored to students. Second, we propose three criteria to evaluate LLM-as-a-tutor specifically designed for EFL writing education, emphasizing pedagogical aspects. In this process, EFL experts evaluate the feedback from LLM-as-a-tutor regarding (1) quality and (2) characteristics. On the other hand, EFL learners assess their (3) learning outcomes from interaction with LLM-as-a-tutor. This approach lays the groundwork for developing LLMs-as-a-tutor tailored to the needs of EFL learners, advancing the effectiveness of writing education in this context.