In astrophysics, hard X- and soft gamma-ray polarimetry has had limited development. To date, no dedicated polarimeters have ever been launched into space. However, previous Monte Carlo simulations and prototype experimental studies have been carried out by the authors in order to evaluate the polarimetric performance of pixelised CZT matrices. We have applied this Monte Carlo code to the case of a CZT pixel instrument proposed as a Gamma-ray burst monitor (GRBM) for an X-ray payload on board the International Space Station (ISS): the LOBSTER experiment, which has already successfully passed the ESA Phase A study for a future flight in 2009. Herein we present the results of the study of the 4 detection units that compose the GRBM detector. Each of these units is a 24times12 matrix of CZT elementary crystals and the pixels have a cross section of 8times8 mm2, giving an active area of about 184 cm2 for each unit. The detector thickness is nominally 3 mm, with a maximum of 5 mm should this thickness be crucial to exploit the GRBM as a polarimeter. The 4 detection units have a rectangular FOV of 55degtimes 35deg FWHM and their axes are misaligned with each other by 45deg in the direction perpendicular to the ISS motion and 10deg along the ISS direction of motion. The GRBM will operate in the energy range between 3 keV and 300 keV. The energy dependent polarimetric Q factor and detection efficiencies are presented and the expected minimum detectable polarization for gamma ray bursts is discussed