The Nice model of the dynamical instability and migration of the giant planets can explain many properties of the present solar system, and can be used to constrain its early architecture. In the jumping-Jupiter version of the Nice model, required from the terrestrial planet constraint and dynamical structure of the asteroid belt, Jupiter has encounters with an ice giant. Here, we study the survival of the Galilean satellites in the jumping-Jupiter model. This is an important concern because the ice-giant encounters, if deep enough, could dynamically perturb the orbits of the Galilean satellites and lead to implausible results. We performed numerical integrations where we tracked the effect of planetary encounters on the Galilean moons. We considered three instability cases from Nesvorny & Morbidelli that differed in the number and distribution of encounters. We found that in one case, where the number of close encounters was relatively small, the Galilean satellite orbits were not significantly affected. In the other two, the orbital eccentricities of all moons were excited by encounters, Callisto's semimajor axis changed, and, in a large fraction of trials, the Laplace resonance of the inner three moons was disrupted. The subsequent evolution by tides damps eccentricities and can recapture the moons in the Laplace resonance. A more important constraint is represented by the orbital inclinations of the moons, which can be excited during the encounters and not appreciably damped by tides. We find that one instability case taken from Nesvorny & Morbidelli clearly does not meet this constraint. This shows how the regular satellites of Jupiter can be used to set limits on the properties of encounters in the jumping-Jupiter model, and help us to better understand how the early solar system evolved.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)NASA's Outer Planet Research programCzech Grant AgencyConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)SW Res Inst, Boulder, CO USACharles Univ Prague, Inst Astron, Prague, Czech RepublicUniv Estadual Paulista, Rio Claro, SP, BrazilUniv Estadual Paulista, Rio Claro, SP, BrazilFAPESP: 12/23732-4FAPESP: 10/11109-5Czech Grant AgencyP209-13-013085