  We generalize our recent analysis [2006.13249] of probe string dynamics to
the case of general single-trace $T\bar T$, $J\bar T$ and $T\bar J$
deformations. We show that in regions in coupling space where the bulk geometry
is smooth, the classical trajectories of such strings are smooth and approach
the linear dilaton boundary at either the far past or the far future. These
trajectories give rise to quantum scattering states with arbitrarily high
energies. When the bulk geometry has closed timelike curves (CTC's), the
trajectories are singular for energies above a critical value $E_c$. This
singularity occurs in the region with CTC's, and the value of $E_c$ agrees with
that read off from the dual boundary theory for all values of the couplings and
charges.

High Energy Physics - Theory