  We study the potential of future lepton colliders to probe violation of the
CP symmetry in the top quark sector. In certain extensions of the Standard
Model, such as the two-Higgs-doublet model (2HDM), sizeable anomalous top quark
dipole moments can arise, that may be revealed by a precise measurement of top
quark pair production. We present results from detailed Monte Carlo studies for
the ILC at 500~\GeV{} and CLIC at 380~\gev{} and use parton-level simulations
to explore the potential of high-energy operation. We find that precise
measurements in $e^+e^- \rightarrow t\bar{t}$ production with subsequent decay
to lepton plus jets final states can provide sufficient sensitivity to detect
Higgs-boson-induced CP violation in a viable two-Higgs-doublet model. The
potential of a linear $e^+e^-$ collider to detect CP-violating electric and
weak dipole form factors of the top quark exceeds the prospects of the HL-LHC
by over an order of magnitude.
