The perturbation of the interferometric phase is a corrective term of the measured phase shift that should be taken into account in the measurement of the electron line density in a combined interferometer-polarimeter for the diagnostics of the electron density and the magnetic field in a fusion plasma. In this paper we first review in detail the theory of this effect and present a new and complete derivation of it, which also accounts for some errors published in a previous paper. Then we consider this effect in the interferometer-polarimeter of three different plasma devices: RTP, JET and DTT and for each machine we calculate the expected phase perturbation for a typical plasma profile, especially with reference to the use of the popular three-wave technique for the polarization modulation of the input probing beam.