The extraction of the leptonic charge-parity (CP)-violating phase $\delta_{\rm CP}$ from long-baseline neutrino oscillation experiments rests on the assumption of charge-parity-time (CPT) conservation. We show that CPT violation, parametrized as an asymmetry $\delta \Delta m_{31}^2\equiv \bar{\Delta }{m}_{31}^2-\Delta m_{31}^2$ between neutrino and antineutrino mass splittings, induces an effective, energy-dependent phase shift $\phi_{\rm eff}(E)$ that is functionally degenerate with $\delta_{\rm CP}$ in the appearance asymmetry $⟨\Delta P⟩$. This has a profound implication for long-baseline experiments, where the tension between T2K and NO$\nu$A CPT-conserving best-fit $\delta_{\rm CP}$ values can be significantly alleviated by a CPT-violating truth; and a CPT-conserving fit can miss the true CP phase entirely for $|\delta \Delta m_{31}^2|\gtrsim 0.3\times {10}^{-3}{\mathrm{\text{eV}}}^2$ for DUNE. We then demonstrate that atmospheric neutrino telescopes provide the natural tool to resolve this degeneracy: using existing data from IceCube-DeepCore (7.74 yr) and KM3NeT/ORCA-6 (433 kt-yr), we derive a world-leading constraint on CPT-violation at $|\delta \Delta m_{31}^2|\le 0.57\times {10}^{-3}{\mathrm{\text{eV}}}^2$ at 90% CL. With the IceCube Upgrade and full ORCA detector, we can reach a $1\sigma$ constraint at ${10}^{-4}{\mathrm{\text{eV}}}^2$ within a decade, providing the independent CPT constraint needed to ensure that DUNE’s $\delta_{\rm CP}$ measurement is unambiguous.