We have measured under zero-field-cooled ZFC and field-cooled FC conditions the magnetic moments of a high-quality Pb,Bi2Sr2Ca2Cu3O10y tape at 5 K in perpendicular applied fields up to 1 T using a superconducting quantum interference device magnetometer. The intergranular magnetic moment, obtained by subtracting from the total magnetic moment the intragranular moment of the ''bent'' tape shows a pronounced anomalous peak at a positive field Hp . To interpret the experimental data the critical-state model for a flat superconducting strip in a perpendicular field is employed. The model includes the field dependence of the intergranular critical current density in first order. The field at grain-boundary Josephson junctions, which strongly influences the intergranular current, is estimated by taking the demagnetizing effect of the grains into account. The model predicts correctly the measured intergranular magnetic moments and the behavior of the anomalous peak in both the ZFC and the FC case. The saturation of the remanent intragranular magnetization occurs at a lower maximum field than the saturation of Hp which can be well understood in terms of the demagnetizing effect of the grains. A model which neglects grain demagnetization but instead takes the vortex distribution of vortices near Josephson junctions into account cannot describe quantitatively the observed behavior of the anomalous peak.