Ferroelectric copolymers of polyvinylidene fluoride and trifluoroethylene are attractive gate materials because of a rather high remanent polarization, low dielectric permittivity, and easy integration on semiconductors due to the low processing temperature. Recently it was demonstrated that the functionalities of devices with ferroelectric polymer gates can be extended to magnetic field effect transistors with diluted magnetic semiconductor channels. Here we address the critical issue of polarization screening in such transistors quantifying the amount of polarization charge which controls the magnetic channel. The gate effect is shown to be limited by internal polarization screening rather than polarization retention loss.