Biomimetic and bioinspired design is not only a potent resource for roboticists looking to develop robust engineering systems or understand the natural world. It is also a uniquely accessible entry point into science and technology. Every person on Earth constantly interacts with nature, and most people have an intuitive sense of animal and plant behaviour, even without realizing it. The Natural Robotics Contest is novel piece of science communication that takes advantage of this intuition, and creates an opportunity for anyone with an interest in nature or robotics to submit their idea and have it turned into a real engineering system. In this paper we will discuss the competition's submissions, which show how the public thinks of nature as well as the problems people see as most pressing for engineers to solve. We will then show our design process from the winning submitted concept sketch through to functioning robot, to offer a case study in biomimetic robot design. The winning design is a robotic fish which uses gill structures to filter out microplastics. This was fabricated into an open source robot with a novel 3D printed gill design. By presenting the competition and the winning entry we hope to foster further interest in nature-inspired design, and increase the interplay between nature and engineering in the minds of readers.