We report a study of the pinning properties of Fe/MgB2 tapes performed by means of ac and dc magnetic measurements. In particular, the third harmonic response of the ac susceptibility has been measured as a function of the dc magnetic field up to 9 T, at different temperatures, for various frequencies and amplitudes of the ac field. The irreversibility line has been determined using the third harmonic onset criterion for samples made with different ball milled MgB2 powders. The study of the harmonic response allows to probe the nature of the vortex pinning and to analyze its influence on the enhancement of the irreversibility field in strongly ball-milled samples. We have investigated the dynamic regimes governing the vortex motion in the tapes by comparing the experimental curves with numerical simulations of the nonlinear diffusion equation for the magnetic field. Furthermore, the pinning mechanism governing the electrical transport properties has been determined by studying the magnetic field dependence of the volume pinning force FP=Jc×B, calculated by extracting the critical current density Jc(B,T) from magnetic hysteresis loops. Scaling of the FP(B) curves at different temperatures allows us to establish that the pinning centres are confined to the grain boundaries.