<p>In this work, we establish the nonlinear orbital stability of dark solitons for the modified Korteweg-de Vries hierarchy with nonzero boundary conditions for the first time. Employing the inverse scattering approach allows us to determine the approximation of scattering data associated with the perturbed solution by examining the changes in the initial value. On the other hand, we find that it becomes feasible to reconstruct the solution over time utilizing the aforementioned details on scattering data through the application of Marchenko equations. Given the properties of eigenfunctions and scattering data, the deviation of the solution is manageable via the resolution of Marchenko equations, which exhibit explicit temporal progression, thereby culminating the outcome of orbital stability.</p>