Phase-sensitive amplification of squeezed states is a technique to mitigate high detection loss, which is especially attractive at 2 mu m wavelengths. We derived an analytical model proving that amplified squeezed states can mitigate phase noise significantly. Our model discloses two practical parameters: the effective measurable squeezing and the effective detection efficiency of amplified squeezed states. A realistic case study includes the dynamics of the gain-dependent impedance matching conditions of the amplifier. Our results recommend operating the optical parametric amplifier at high gains because of the signal-to-noise ratio's robustness to phase noise. Amplified squeezed states are relevant in proposed gravitational wave detectors and interesting for applications in quantum systems degraded by the output coupling loss in optical waveguides.