Among the rare earth titanates and stannates cristallising in the pyrochlore crystal structure, Tb2Ti2O7 is a singular system since its ground state is believed to be a spin liquid state. As such, it attracts a lot of interest because this state is believed to potentially exhibit new states of matter including quantum effects. Although Tb2Ti2O7 has been the subject of several studies in the last decade, including by muSR, our recent work has shown several features which have been overlooked so far. With this proposal, we intend to address the question of the muSR spin liquid signature and the possible existence of a magnetic transition at low temperature in some specimen of Tb2Ti2O7.