Continuous-variable quantum key distribution (CVQKD) can be effectively compatible with off-the-shelf communication systems and has been proven to be the security against collective attacks in the finite-size regime and composability. In this paper, we classify three different trust levels for the loss and noise experienced by the sender and receiver. Based on these trust levels, we derive the composable finite-size security bounds of inter-satellite CVQKD in the terahertz (THz) band. We also show how these trust levels can nontrivially increase the composable secret key rates of THz-CVQKD and tolerate higher loss. Furthermore, the numerical simulations strongly support the feasibility of inter-satellite THz-CVQKD even in the worst trust level. This work provides an efficient path for building an inter-satellite quantum communication network.