  We consider a model of boosted dark matter (DM), where a fraction of DM is
upscattered to relativistic energies by cosmic ray electrons. Such interactions
responsible for boosting the DM also attenuate its flux at the Earth.
Considering a simple model of constant interaction cross-section, we make
analytical estimates of the variation of the attenuation ceiling with the DM
mass and confirm it numerically. We then extend our analysis to a $Z'$-mediated
leptophilic DM model. We show that the attenuation ceiling remains nearly
model-independent for DM and mediator particles heavier than the electron,
challenging some previous discussions on this topic. Using the XENONnT direct
detection experiment, we illustrate how constraints based on energy-dependent
scattering can significantly differ from those based on an assumed constant
cross-section. This highlights the importance of re-evaluating these
constraints in the context of specific models.
