The segmentation of reflections from the iris region is a relevant task for biometric systems, human-machine interaction technologies, and photo editing applications. This task is particularly complex for ocular images acquired from uncooperative users in uncontrolled illumination and environmental conditions. Furthermore, to the best of our knowledge, all of the studies in the literature on methods specifically designed to detect reflections in the iris texture are based on algorithmic approaches. In this paper, we present the first study on deep neural networks for segmenting reflection regions from iris images. Specifically, we propose a modified version of the U-Net architecture based on an encoder (downsampler) characterized by a relatively low computational complexity, and designed with the aim of being applied on edge devices. Experiments have been performed for a dataset of 3,286 ocular images acquired from websites and social media in completely uncontrolled and uncooperative conditions. The obtained results prove that our proposed method can accurately segment the iris reflections for particularly challenging images. A detailed qualitative analysis also confirm the robustness of our method for non-ideal application contexts. Furthermore, experiments show that our method can increase the accuracy of state-of-the-art iris segmentation techniques based on deep neural networks.