The dynamics of globular cluster systems (GCSs) around galaxies are often used to assess the total enclosed mass, and even to constrain the dark matter distribution. The GCS of a galaxy is typically assumed to be in dynamical equilibrium within the potential of the host galaxy. However cluster galaxies are subjected to a rapidly evolving and, at times, violently destructive tidal field. We investigate the impact of the harassment on the dynamics of GCs surrounding early-type cluster dwarfs, using numerical simulations. We find that the dynamical behaviour of the GCS is strongly influenced by the fraction of bound dark matter fDM remaining in the galaxy. Only when fDM falls to ˜15 per cent do stars and GCs begin to be stripped. Still the observed GC velocity dispersion can be used to measure the true enclosed mass to within a factor of 2, even when fDM falls as low as ˜3 per cent. This is possible partly because unbound GCs quickly separate from the galaxy body. However even the distribution of bound GCs may spatially expand by a factor of 2-3. Once fDM falls into the <3 per cent regime, the galaxy is close to complete disruption, and GCS dynamics can no longer be used to reliably estimate the enclosed mass. In this regime, the remaining bound GCS may spatially expand by a factor of 4 to 8. It may be possible to test if a galaxy is in this regime by measuring the dynamics of the stellar disc. We demonstrate that if a stellar disc is rotationally supported, it is likely that a galaxy has sufficient dark matter that the dynamics of the GCS can be used to reliably estimate the enclosed mass.