Polarization-mode dispersion (PMD) and polarization-dependent loss (PDL) associated with various optical components affect the quality of pump beams even before they enter a fiber-optic parametric amplifier (FOPA). A vector theory of the underlying four-wave mixing process is developed to study the impact of PMD and PDL on the amplification of signal and idler fields. It is shown that the use of high-quality polarizers just before the input end of the fiber can improve the performance of a dual-pump parametric amplifier considerably.