  We study the impact of non-zero (and apparently large) value of the nucleon
mass $M$ on the shape of parton quasi-distributions $Q(y,p_3)$, in particular
on its change with the change of the nucleon momentum $p_3$. We observe that
the usual target-mass corrections induced by the $M$-dependence of the twist-2
operators are rather small. Moreover, we show that within the framework based
on parametrizations by transverse momentum dependent distribution functions
(TMDs) these corrections are canceled by higher-twist contributions. We
identify a novel source of kinematic target-mass dependence of TMDs and build
models corrected for such dependence. We find that resulting changes may be
safely neglected for $p_3 \gtrsim 2M$.
