An extensive study of the magnetic properties of FeTe0.7Se0.3 crystals in the superconducting state is presented. We show that weak collective pinning, originating from spatial variations of the charge carrier mean free path (δl pinning), rules in this superconductor. Our results are compatible with the nanoscale phase separation observed on this compound and indicate that in spite of the chemical inhomogeneity, spatial fluctuations of the critical temperature are not important for pinning. A power-law dependence of the magnetization vs time, generally interpreted as the signature of a single-vortex creep regime, is observed in magnetic fields up to 8 T. For magnetic fields applied along the c axis of the crystal, the magnetization curves exhibit a clear peak effect whose position shifts when varying the temperature, following the same dependence as observed in YBa2Cu3O7−δ. The time and temperature dependence of the peak position has been investigated. We observe that the occurrence of the peak at a given magnetic field determines a specific vortex configuration that is independent on the temperature. This result indicates that the influence of the temperature on the vortex-vortex and vortex-defect interactions leading to the peak effect in FeTe0.7Se0.3 is negligible in the explored range of temperatures.