This letter is concerned with the preservation of privacy in remote state estimation of cyber-physical systems. A privacy-preserving transmission scheduling strategy against eavesdropping is proposed, incorporating three operational modes for sensors: silence, direct transmission, and noise-injected transmission. This strategy is designed to minimize the transmission cost and estimation error covariance for the remote estimator while maximizing the estimation error covariance for eavesdroppers. Threshold structures are demonstrated for optimal transmission schedules in different scenarios. Additionally, a novel correlation between the optimal transmission choice and the magnitude of injection noise is presented, particularly pertinent to scenarios involving direct transmission and transmission with injection noise. This correlation is important in balancing transmission information integrity against privacy concerns. Finally, several numerical examples are presented to demonstrate the effectiveness of the theoretical results.