Using Monte Carlo simulations, we study a coarse-grained model of a water layer confined in a fixed disordered matrix of hydrophobic nanoparticles at different particle concentrations c. For c=0, we find a first-order liquid-liquid phase transition (LLPT) ending in one critical point at low pressure P. For c>0, our simulations are consistent with a LLPT line ending in two critical points at low and high P. For c=25%, at high P and low temperature, we find a dramatic decrease of compressibility, thermal expansion coefficient, and specific heat. Surprisingly, the effect is present also for c as low as 2.4%. We conclude that even a small presence of hydrophobic nanoparticles can drastically suppress thermodynamic fluctuations, making the detection of the LLPT more difficult.