Linear geo-textures are widely recognized on synthetic scaled images of planetary surfaces and consist of elongated alignments of tonal contrasts. When these linear patterns are clustered in azimuthal sets and organized in domains occurring on specific terranes, they reflect the structural grain of the crust and provide clues on the stress trajectories. In this way, the geostatistical analysis of lineament domains represents a useful tool to highlight the geotectonic settings of planetary surfaces. In this work, we applied a lineament domain analysis to better frame the tectonic evolution of the Claritas Fossae (CF) area on Mars, the origin of which is still debated, and both dip–slip and strike–slip tectonics have been described in the literature. A twofold approach was followed that included the identification of a linear pattern with manual and automatic approaches. The automatic method confirmed and validated the results of the manual detection. The statistical analysis of the identified lineaments showed their clustering in two domains that persisted on different terranes separated by the regionally sized scarp associated with the CF. This scarp is the surface manifestation of the CF crustal fault. The spatial distribution of the two domains and their constant angular relationship of about 30° allowed relating one domain to the main CF fault and the other domain to the extensional deformation associated with the fault kinematics. Our results suggest that the CF frames well within a regional setting characterized by right–lateral kinematics with about 20% transtension. Temporal constraints derive from the ages of the terrains where the two domains develop. On this basis, we propose that a first tectonic event occurred in the Noachian age followed by a reactivation occurring after the emplacement of the Late Hesperian lavas.