High‐obliquity excursions on Mars are hypothesized to have redistributed water from the poles to nourish mid‐latitude glaciers. Evidence of this process is provided by different types of viscous flow features (ice‐rich deposits buried beneath sediment mantle) located there today, including lobate debris aprons (LDAs). During high‐obliquity extremes, ice may have persisted even nearer the equator, as indicated by numerous enigmatic depressions bounded on one side by either isolated mesas or scarps, and on the other by a lava unit. These depressions demarcate the past interaction between flowing lava and ghost LDAs (GLDAs), which have long since disappeared. We term these features GLDA depressions, about which little is known besides their spatial extent. This collection of depressions implies tropical ice loss over an area ∼100,000 km2. To constrain their history in Kasei Valles, we derive model ages for GLDA depressions, mesas, and the lava flow from crater counts. We use a 2D model of glacial ice constrained by the topography of GLDA depressions to approximate the surface and volume of former glacial ice deposits. The model reconstructs former ice surfaces along multiple flow lines orientated normal to GLDA depression boundaries. This reconstruction indicates that 1,400–3,500 km3 of ice—similar to that present in Iceland on Earth—existed at ∼1.3 Ga when the lava was emplaced. Dating shows that the GLDAs survived for up to ∼1 billion years following lava emplacement, before its final demise.