Legal Implications of Implicit Acceptance of Internship Appointment Letter

I started working as an intern at a company without signing their appointment letter. The email along with appointment letter states that if I do not sign, it will be assumed that I have accepted the terms post 1 day of email. I worked for only two days before resigning and returned all company property, with verbal confirmation from the HR allowing me to leave for the day from the office. The appointment letter includes a clause stating: "If an intern wishes to resign during the internship, the notice period of the same shall be determined at the sole discretion of the Company." The company on the next day is now claiming that my resignation is invalid and is pressuring me to comply with their demands, including visiting their office. I have not signed any formal agreement, and I communicated my resignation in writing. Could you please clarify: 1. Am I legally bound to the terms of the appointment letter despite not signing it? 2. Does the clause about the notice period being at the company's discretion hold any legal weight, especially since I worked for only two days? 3. How can I protect myself if the company threatens to escalate this matter to my college regarding my degree or threatens legal action? Thank you for your guidance.