  We consider fermionic (Dirac or Majorana) cold thermal relic dark-matter
coupling to standard-model particles through the effective dimension-5 Higgs
portal operators $\Lambda^{-1} \ \mathcal{O}_{\text{DM}} \cdot H^\dagger H$,
where $\mathcal{O}_{\text{DM}}$ is an admixture of scalar $\bar\chi\chi$ and
pseudoscalar $\bar\chi i\gamma_5 \chi$ DM operators. Utilizing the relic
abundance requirement to fix the couplings, we consider direct detection and
invisible Higgs width constraints, and map out the remaining allowed parameter
space of dark-matter mass and the admixture of scalar and pseudoscalar
couplings. We emphasize a subtlety which has not previously been carefully
studied in the context of the EFT approach, in which an effect arising due to
electroweak symmetry breaking can cause a na\"ively pure pseudoscalar coupling
to induce a scalar coupling at higher order, which has important implications
for direct detection bounds. We provide some comments on indirect detection
bounds and collider searches.
