  Arina et al. have proposed the Dirac fermionic dark matter with
pseudoscalar-mediated interactions to explain the Galactic Center excess,
correct relic density and DAMA signal. They have assumed that contact
interactions remain roughly valid in calculating scattering rates at the direct
detection even when the mediator mass is the same order as the typical momentum
transfer. We show that such a replacement is not suitable. Adopting the full
form of interactions, we show that the gamma-ray excess allowed parameters are
completely outside of the DAMA iodine 3$\sigma$ region, even for
heavy-flavor-universal couplings, for which $m_{DM} \sim 40$ GeV in the
gamma-ray excess fit. As for Higgs-like couplings, the two regions overlap for
$m_a\lesssim$ 15 MeV, where long-range interactions, instead of contact
interactions, occur at the DAMA.
