When a metal at a higher temperature is transferred to water at a lower temperature, heat is inevitably lost to the calorimeter. how does this heat loss change the value of the calculated specific heat compared to the actual specific heat?

Because of the Law of Conservation of Energy, the heat loss plus the heat used to combust the sample should calculate to the actual heat capacity. A calorimeter is ideally an insulated vessel. However, in reality, heat is dissipated. Therefore, the heat capacity that we calculate in the experiment will always be less than the actual value. This is accounted by the heat lost.