Context. IRAS 16293E is a rare case of a prestellar core being subjected to the effects of at least one outflow.Aims. We want to disentangle the actual structure of the core from the outflow impact and evaluate the evolutionary stage of the core.Methods. Prestellar cores being cold and depleted, the best tracers of their central regions are the two isotopologues of the trihydrogen cation that are observable from the ground: ortho-H2D+ and para-D2H+. We used the Atacama Pathfinder EXperiment (APEX) telescope to map the para-D2H+ emission in IRAS 16293E and collected James Clerk Maxwell Telescope (JCMT) archival data of ortho-H2D+. We compared their emission to that of other tracers, including dust emission, and analysed their abundance with the help of a 1D radiative transfer tool. The ratio of the abundances of ortho-H2D+ to para-D2H+ can be used to estimate the stage of the chemical evolution of the core.Results. We have obtained the first complete map of para-D2H+ emission in a prestellar core. We compare it to a map of ortho-H2D+ and show their partial anti-correlation. This reveals a strongly evolved core with a para-D2H+/ortho-H2D+ abundance ratio towards the centre for which we obtain a conservative lower limit from 3.9 (at 12 K) to 8.3 (at 8 K), while the high extinction of the core is indicative of a central temperature below 10 K. This ratio is higher than predicted by the known chemical models found in the literature. Para-D2H+ (and indirectly ortho-H2D+) is the only species that reveals the true centre of this core, while the emission of other molecular tracers and dust are biased by the temperature structure that results from the impact of the outflow.Conclusions. This study is an invitation to reconsider the analysis of previous observations of this source and possibly questions the validity of the deuteration chemical models or of the reaction and inelastic collisional rate coefficients of the H+3 isotopologue family. This could impact the deuteration clock predictions for all sources.