Eye-tracking (ET) is one of the most intuitive solutions for enabling people with severe motor impairments to control devices. Nevertheless, even such an effective assistive solution can detrimentally affect user experience during demanding tasks because of, for instance, the user's mental workload - using gaze-based controls for an extensive period of time can generate fatigue and cause frustration. Thus, it is necessary to design novel solutions for ET contexts able to improve the user experience, with particular attention to its aspects related to workload. In this paper, a pilot study evaluates the effects of a relaxation biofeedback system on the user experience in the context of a gaze-controlled task that is mentally and temporally demanding: ET-based gaming. Different aspects of the subjects' experience were investigated under two conditions of a gaze-controlled game. In the Biofeedback group (BF), the user triggered a command by means of voluntary relaxation, monitored through Galvanic Skin Response (GSR) and represented by visual feedback. In the No Biofeedback group (NBF), the same feedback was timed according to the average frequency of commands in BF. After the experiment, each subject filled out a user experience questionnaire. The results showed a general appreciation for BF, with a significant between-group difference in the perceived session time duration, with the latter being shorter for subjects in BF than for the ones in NBF. This result implies a lower mental workload for BF than for NBF subjects. Other results point toward a potential role of user's engagement in the improvement of user experience in BF. Such an effect highlights the value of relaxation biofeedback for improving the user experience in a demanding gaze-controlled task.