Lower atmospheric global dust storms affect the small- and large-scale weather and variability of the whole Martian atmosphere. Analysis of the CO2 density data from the Neutral Gas and Ion Mass Spectrometer instrument (NGIMS) on board NASA’s Mars Atmosphere Volatile EvolutioN (MAVEN) spacecraft show a remarkable increase of GW-induced density fluctuations in the thermosphere during the 2018 major dust storm with distinct latitude and local time variability. The mean thermospheric GW activity increases by a factor of two during the storm event. The magnitude of relative density perturbations is around 20% on average and 40% locally. One and a half months later, the GW activity gradually decreases. Enhanced temperature disturbances in the Martian thermosphere can facilitate atmospheric escape. For the first time, we estimate that, for a 20% and 40% GW-induced disturbances, the net increase of Jeans escape flux of hydrogen is a factor of 1.3 and 2, respectively.