The Open University has a large set of plugins for Moodle available from the plugin database at Moodle.org, among the set is a simple tool that might help to discourage dishonesty and plagiarism in quizzes. The plugin is the Acknowledge Plagiarism Statement Access Rule [https://moodle.org/plugins/view.php?plugin=quizaccess_honestycheck] which presents students with a disclaimer and checkbox to “agree” prior to starting a quiz (if the quiz is configured to include the statement).
Think of it as a “Agree to these Terms” type action, but for any quiz where you’d like it and always as an additional set that must be acknowledged.
While not a technical measure like Turnitin or proctoring, honor codes and acknowledgement of plagiarism agreements and student ethical/honesty contracts have long been thought to help in discouraging cheating in online and face to face courses alike. One of several tools that I encourage you to consider as you manage courses through any learning management system.
Download it here: https://moodle.org/plugins/view.php?plugin=quizaccess_honestycheck