  In this letter we revisit general dark matter (DM)-bound-electron
interactions studied previously in the influential work of [Catena et al.,
Phys. Rev. Res. 2, 033195 (2020)]. We derive the DM-electron response functions
and find a crucial minus sign was missed for the second atomic response
function $W_2$ defined in that work. The minus sign has significant
phenomenological consequences when explaining experimental bounds on specific
DM scenarios. Furthermore, for the most general DM-electron nonrelativistic or
relativistic interactions for DM with spin up to one, we find there are three
DM response functions ($a_{0,1,2}$) whose corresponding atomic response
functions ($\widetilde W_{0,1,2}$) are linear combinations of the four response
functions ($W_{1,2,3,4}$) given in that work, $$ \widetilde W_0 = W_1, \,
\widetilde W_2 = |\mathbf{v}_0^\perp|^2 W_1+ W_3 - 2 {m_e\, \mathbf{q}\cdot
\mathbf{v}_0^\perp \over \mathbf{q}^2} W_2,\, \widetilde W_3 = {
(\mathbf{q}\cdot \mathbf{v}_0^\perp)^2 \over \mathbf{q}^2} W_1 + {m_e^2 \over
\mathbf{q}^2}W_4 - 2 {m_e\, \mathbf{q}\cdot \mathbf{v}_0^\perp \over
\mathbf{q}^2} W_2. $$ Due to the minus sign correction for $W_2$, there can be
significant cancellations between the $W_2$ and $W_{3,4}$ terms, so that
$\widetilde W_{2,3}$ are dominated by the usual response function $W_1$ in some
cases. Ignoring the sign could thus result in misinterpretation of the
experimental data in some DM scenarios. As an example, we show that the recent
XENON1T constraint on the fermionic DM anapole moment is weakened by a factor
of 2 or so. Many DM scenarios involving DM or electron axial-vector current can
yield $W_2$ and thus are potentially affected by the sign.
