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The action of tidal friction, coupled with the Kozai cycles, drastically changed the original orbits of trans-Neptunian binaries (TNBs). The dynamics of the Kozai mechanism is driven by the solar torque on the mutual orbit, so that the orientation of the latter relative to the heliocentric orbital plane plays a fundamental role in this process, both in the magnitude and in the characteristic of the cycles. In this way, any effect that makes this relative orientation vary may be relevant in the dynamics of the process. In this paper, we will focus on the effect that the perturbations of the giant planets on the heliocentric orbit of TNBs have on the dynamics of the Kozai cycles and tidal friction. For this task, we have performed numerical simulations of the evolution of a synthetic population of TNBs subject to Kozai cycles and tidal friction adding planetary perturbation on their heliocentric orbits. We found that in a non-negligible fraction of cases (∼25 per cent), this additional perturbation produces substantial changes in the orbital evolution. The slow precession of the heliocentric orbit and the variation of its inclination can make the dynamical evolution of the mutual orbits very irregular, completely changing the morphology of the Kozai cycles. When these variations are coupled to tidal friction, the lifetime of the TNBs can change substantially.