A coherence-controlled holographic microscope (CCHM) enables quantitative phase imaging with coherent as well as incoherent illumination. The low spatially coherent light induces a coherence gating effect, which makes observation of samples possible also through scattering media. The paper describes theoretically and simulates numerically imaging of a two-dimensional object through a static scattering layer by means of CCHM, with the main focus on the quantitative phase imaging quality. The authors have investigated both strongly and weakly scattering media characterized by different amounts of ballistic and diffuse light. It is demonstrated that the phase information can be revealed also for the case of the static, strongly scattering layer. The dependence of the quality of imaging process on the spatial light coherence is demonstrated. The theoretical calculations and numerical simulations are supported by experimental data gained with a model phase object, as well as living carcinoma cells treated in an optically turbid emulsion.