Iron based high temperature superconductors have several common features with superconducting cuprates, including the square lattice and the proximity to an antiferromagnetic phase. The magnetic excitation spectrum below T-c of Fe1.02Te0.7Se0.3 shows an hourglass-shaped dispersion with a resonance around the commensurate point. In a previous inelastic neutron scattering study, we showed that the hourglass-shaped dispersion is most likely a prerequisite for superconductivity, while the consequences are the opening of a gap and a shift of spectral weight. In this paper we follow the evolution of the hourglass shaped dispersion under applied pressure up to 12 kbar. Our results show that that the pressure-induced 37% increase of T-c is concomitant with a change in the magnetic excitation spectrum, with an increase of the hourglass energy by 38%.