The sub-leading power of the scattering amplitude for deeply-virtual Compton scattering (DVCS) off the nucleon contains leading-twist and twist-3 generalized parton distributions (GPDs).  We point out that in DVCS, at twist-3 accuracy, one cannot address any individual quark twist-3 GPD.  Accessible are exclusively linear combinations involving both vector and axial-vector twist-3 GPDs.  This implies, in particular, that in DVCS there is no direct access to the (kinetic) orbital angular momentum of quarks through twist-3 GPDs.  Moreover, using the quark-target model, we find that twist-3 GPDs can be discontinuous.  The discontinuities however vanish in the DVCS amplitude, which further supports the hypothesis of factorization at twist-3 accuracy.