In this work, we use N-body simulations performed on GPU to trace the past 10 Gyr dynamical history of a globular cluster (GC) similar to NGC 6397 in the tidal field of a Milky Way-like galaxy and we compare our simulated GCs with data from the third Gaia early data release. Our simulations predict, in contrast to what is deduced from the data, that such a cluster should present strong and extended tidal tails by more than 6 Gyr ago (right after the first third of its life), exceeding 1 kpc of length, and should be roughly disrupted by current time. We analysed each of our initial conditions, such as initial mass and density parameters, as well as the dark matter shape, and we argue that the most likely reason for such discrepancy between the data and our simulations is related to the fact that we consider a purely baryonic cluster in the beginning of each model we test. We discuss that if our globular cluster was initially embedded in a dark matter minihalo, the latter could act as a protecting envelope, which prevents the tidal stripping of the luminous matter, while being itself gradually disrupted and removed in the course of the cluster evolution. This could explain why an insignificant amount of dark matter is required to describe the velocity dispersion in NGC 6397, up to at least a few half-mass radii.