Turkish Airlines Pet Travel Issue on Gaziantep-Dalaman Flight

I had a ticket for the 05:45 Gaziantep-Dalaman flight. Despite including my pet in my ticket and having all vaccinations up to date, I was informed during check-in that my pet could not be accepted on the flight because its cage was not a hard cage. However, when I reviewed Turkish Airlines' Pet Travel Rules, I did not find such a restriction, nor was I warned about this when purchasing the ticket. In the end, I was told that I would receive an unreasonable refund of ₺70. When I requested a ticket change, the staff suggested that I leave my pet at the airport and continue my journey. This attitude from a well-known company like Turkish Airlines is unacceptable. Despite being at the airport 45 minutes before the flight and having a cage that meets the specified requirements, I demand that my grievance be addressed.