Injection-and-recovery test performed to check the detectability of the innermost planets GJ 273b and GJ 273c in the current set of TESS data. We injected synthetic transits into the available photometric data corresponding to each planet by taking into account the uncertainties in their physical properties. We explored a total of1080 different scenarios. We found that planet GJ 273c showed a recovery rate of 100%, which clearly suggests that this planet is not transiting. On the other hand, planet GJ 273b showed a recovery rate of ~ 40%, implying its possible detection in future observations. We carried out two other experiments to check the detectability of the two outermost planets GJ 273d and GJ 273e, finding recovery rates < 2%; see the main text for more details.