Is it strange to wear high-heel sandals as a private tutor?

Hello. I (35F) am a private tutor and I have quite a few students I work with. We always have the lessons at my students’ houses. The other day, I went to my parents’ house before an afternoon class. I was wearing high-heel sandals (more precisely, wedge sandals). Actually, I often wear my wedge sandals to tutoring sessions.

My dad pointed out that my outfit might seem too 'chic' for a tutoring session. I never thought of it that way because I always dress modestly. That day, I was wearing a sweater with jeans, and I take my sandals off inside the houses and go barefoot. I had no intention of being provocative or trying to look attractive for my students in any way.

However, now I am anxious that wearing high-heel sandals could be misinterpreted. Am I wrong for doing that?