Peer-feedback efficiency might be influenced by the oftentimes voiced concern of students that they perceive their peers' competence to provide feedback as inadequate. Feedback literature also identifies mindful processing of (peer)feedback and (peer)feedback content as important for its efficiency, but lacks systematic investigation. In a 2 × 2 factorial design, peer-feedback content (concise general feedback [CGF] vs. elaborated specific feedback [ESF]) and competence of the sender (high vs. low) were varied. Students received a scenario containing an essay by a fictional student and fictional peer feedback, a perception questionnaire, and a text revision, distraction, and peer-feedback recall task. Eye tracking was applied to measure how written peer feedback was (re-)read, e.g., glance duration on exact words and sentences. Mindful cognitive processing was inferred from the relation between glance duration and (a) text-revision performance and (b) peer-feedback recall performance. Feedback by a high competent peer was perceived as more adequate. Compared to CGF, participants who received ESF scored higher on positive affect towards the peer feedback. No effects were found for peer-feedback content and/or sender's competence level on performance. Glance durations were negatively correlated to text-revision performance regardless of condition, although peer-feedback recall showed that a basic amount of mindful cognitive processing occurred in all conditions. Descriptive findings also hint that this processing might be dependent on an interaction between peer-feedback content and sender's competence, signifying a clear direction for future research.