Do people exercise their right to renew monthly rent contracts via KakaoTalk or certified mail?

To be honest, there has been some trouble, so I notified them that they couldn't extend the lease because I planned to rent the unit to someone else and my parents were going to live there. However, I just received a KakaoTalk message stating that they are exercising their right to renew the contract via certified mail and KakaoTalk.
The certified mail demands a written confirmation that my parents will actually be moving in, and it states that if the unit is rented to a third party, they will claim damages such as moving expenses.
This is becoming quite a headache.