<p>The production of <i>τμ</i> pairs in electron-positron collisions offers a powerful probe of lepton flavor violation. In this work, we calculate the <i>e</i>⁺<i>e</i>⁻ → <i>τμ</i> cross section within the framework of the Standard Model Effective Field Theory, allowing for arbitrary <i>e</i>⁺<i>e</i>⁻ beam polarizations. We then estimate the sensitivities of proposed future linear colliders, ILC and CLIC, to effective lepton flavor-violating interactions. The high center-of-mass energies achievable at these machines provide particularly strong sensitivity to four-fermion operators. Furthermore, the polarization of the <i>e</i>⁺<i>e</i>⁻ beams enables novel tests of the chirality structure of these interactions. We find that our projected sensitivities not only complement but in certain scenarios surpass those achievable with low-energy tau decay measurements at Belle II.</p>