In the realm of dynamical systems theory, shadowing plays a crucial role. Structurally stable diffeomorphisms exhibit a noteworthy characteristic known as the inverse shadowing characteristic, which is investigated within the context of continuous methods. On compact manifolds, hyperbolic homeomorphisms are demonstrated to possess both inverse shadowing and bi-shadowing characteristics, particularly concerning a class of δ methods. These methods are described as continuous mappings from the manifold into the space of bi-infinite sequences within the manifold, utilizing the product topology. Additionally, the shadowing characteristic of the Lipschitz inverse is explored concerning two distinct classes of approaches, which produce pseudo-trajectories for dynamical systems. In our research, we establish that the characteristic of inverse shadowing can be derived from several fundamental dynamical system characteristics, including structural stability, transversality, Anosov characteristics, expansivity, continuum-wise expansiveness, and expansion.