  Vesta is the only currently identified asteroid for which we possess samples,
which revealed us that the asteroid is differentiated and possesses a
relatively thin basaltic crust that survived to the evolution of the asteroid
belt and the Solar System. However, little is know about the effects of past
events like the Late Heavy Bombardment on this crust. We address this gap in
our knowledge by simulating the LHB in the different dynamical scenarios
proposed for the migration of the giant planets in the broad framework of the
Nice Model. The results of simulations generate information about produced
crater population, surface saturation, mass loss and mass gain of Vesta and
number of energetic or catastrophic impacts during LHB. Our results reveal that
planet-planet scattering is a dynamically favourable migration mechanism for
the survival of Vesta and its crust. The number of impacts on Vesta estimated
as due to the LHB is $31\pm5$, i.e. about 5 times larger than the number of
impacts that would have occurred in an unperturbed main belt in the same time
interval. The contribution of a possible extended belt, instead, is quite
limited and can be quantified in $2\pm1$ impacts. The chance of energetic and
catastrophic impacts is less than 10\% and is compatible with the absence of
giant craters dated back to 4 Ga ago and with the survival of the asteroid
during the LHB. The mass loss translates in the erosion of $3-5$ meters of the
crust, consistently with the global survival of the basaltic crust of Vesta
confirmed by the Dawn mission. Our analysis revealed that the contribution of
the LHB to the cratering of Vesta' surface is not significant and is actually
erased by the crater population produced by the following 4 Ga of collisional
evolution of the asteroid, in agreement with the data provided by the Dawn
mission.
