Thin slumped glass foils are considered good candidates for the realization of future X-ray telescopes with large effective area and high spatial resolution. However, the hot slumping process affects the glass strength, and this can be an issue during the launch of the satellite because of the high kinematical and static loads occurring during that phase. In the present work we have investigated the possible use of Gorilla® glass (produced by Corning®), a chemical tempered glass that, thanks to its strength characteristics, would be ideal. The un-tempered glass foils were curved by means of an innovative hot slumping technique and subsequently chemically tempered. In this paper we show that the chemical tempering process applied to Gorilla® glass foils does not affect the surface micro-roughness of the mirrors. On the other end, the stress introduced by the tempering process causes a reduction in the amplitude of the longitudinal profile errors with a lateral size close to the mirror length. The effect of the overall shape changes in the final resolution performance of the glass mirrors was studied by simulating the glass foils integration with our innovative approach based on glass reinforcing ribs. The preliminary tests performed so far suggest that this approach has the potential to be applied to the X-ray telescopes of the next generation.