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, which may be revealed by a precise measurement of top quark pair production. We present results from detailed Monte Carlo studies for the ILC at Formula omitted and CLIC at Formula omitted and use parton-level simulations to explore the potential of high-energy operation. We find that precise measurements in Formula omitted 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 Formula omitted 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.