Quasi-satellite orbits (QSOs) are orbits around the smaller primary in three-body systems. The MMX mission (developed by JAXA, to be launched in 2024) will use QSOs to orbit Phobos, before landing on its surface. This work studies the feasibility of using the invariant manifolds of three-dimensional QSOs for designing landing trajectories, using the Mars-Phobos system as a case study. Applying continuation and bifurcation-analysis techniques, different families of QSOs were computed and their invariant manifolds propagated. Using a set of favorable manifolds as a reference, multiple maneuvers were designed via multiple-shooting and optimization techniques, producing feasible landing trajectories. The robustness of these trajectories was analyzed using a stability index and Monte Carlo simulations. It was found that using the invariant manifolds of QSOs to land is only possible for some families of QSOs. However, for these, the manifolds allow generating robust and propellant-efficient landing trajectories that are able to reach most of Phobos' surface.