The magnetic hysteresis loop of a granular high-temperature superconductor (HTSC) is determined both by the pinning of Abrikosov vortices in granules and by the penetration and trapping of a magnetic flux in the region of boundaries between granules. The subsystem of the intergranular boundaries of a granular HTSC is a Josephson medium, therefore, the trapped flux in it is Josephson vortices. Meissner currents shielding the external magnetic field cross the intergranular boundaries, which, together with the influence of pinned Josephson vortices, causes the so-called "small" magnetic hysteresis from the subsystem of intergranular boundaries. The properties of the small magnetic hysteresis of granular HTSC Y-Ba-Cu-O systems are studied in detail and described. Experimental conditions, including the magnetic background, have been determined in which the contribution of small hysteresis to the total magnetization of granular HTSC is significant or becomes vanishingly small. An explanation is given for the different manifestation of the contribution of small hysteresis at different magnetic prehistory. In conditions where the remanent magnetization is determined only by the trapping of the flux in the intergranular boundaries, the relaxation of magnetization associated with the dissipation of Josephson vortices is measured. The similarity and difference of such relaxation with the known relaxation associated with the dissipation of Abrikosov vortices are indicated. The shape of the small magnetic hysteresis loop was described using the critical state model. Keywords: granular high-temperature superconductor, magnetic hysteresis, Josephson vortices, magnetization relaxation, pinning.