Integrated terrestrial and non-terrestrial networks (TNTNs) have become a promising architecture for enabling ubiquitous connectivity. Smart remote sensing is one of the typical applications of TNTNs that collects and analyzes various dimensions of remote sensing data by deploying Internet of Things (IoT) sensors and edge computing in terrestrial, space, aerial, and underwater networks. To improve the analysis accuracy of remote sensing data, the owners of different networks should conduct collaborative learning on different dimensions of data, while data and label privacy should be jointly considered. However, the existing collaborative learning paradigms have difficulty in meeting this demand. In this article, we propose a paradigm of split learning (SL), where the data owner and the label owner train different parts of the deep learning model and only exchange the intermediate data (i.e., smashed data and cut layer gradients). We explore the potential privacy attacks that recover the raw data and label information based on the intermediate data and propose the differential privacy (DP) based defense mechanisms that inject randomly generated Laplace noise into the intermediate data to disturb the attack performance. We also conduct a simulation study based on a real-world satellite remote sensing dataset to prove that the SL paradigm with defense mechanisms can effectively balance the performance of the collaborative model training and the protection of the data and label privacy. Finally, we discuss the main challenges and potential research directions of the privacy-preserving SL paradigm for smart remote sensing over TNTNs.