The social ability of humans to provide active feedback during conversations is known as backchannelling. Recent work has recognised the importance of endowing robots with such social behaviour to make interactions more natural. Nonetheless, very little is known about how backchannelling should be designed in order to be detected and whether it can have an impact on users’ behaviour and performance in cooperative tasks. In this article, we aim at evaluating the legibility of robot’s backchannelling behaviour on Persons with Dementia (PwDs) and its effect on their performance when playing cognitive training exercises. Aiming to do so, a TIAGo robot was endowed with backchannelling behaviour generated by combining verbal and non-verbal cues. To evaluate our system, two user studies were carried out, in which the social signal was provided first by a human therapist and later on by a robot. Results indicate that patients were capable of identifying such kind of feedback. Nonetheless, our findings pointed out a significant difference in terms of performance between the two studies. They reveal how patients in the study with the robot overused the feedback to obtain the correct answer, putting in place a cheating mechanism that has led them to significantly worsen their performance. We conclude our work by discussing the implications of our findings when deploying robots in sensitive roles and possible solutions to address such unexpected behaviours.