We propose a kernel-based adaptive filtering method to suppress the phase noise (PN) arising from small deviations from ideal counter-phasing in the dual-pump fibre-based optical phase conjugation (OPC) of pilot-free quadrature-amplitude modulation (QAM) signals. We demonstrate experimentally and numerically that the proposed scheme achieves signal-to-noise ratio improvement over conventional PN compensation under optimised pump dithering settings in the OPC device and features no performance penalty across a range of pump-phase mismatch values, when it is used with a 16-QAM signal in an optical back-to-back configuration. We also illustrate the applicability of the method to the 64-QAM modulation format, and evaluate its performance in a transmission setup with mid-link OPC by means of numerical simulations.