Catch shares are being increasingly adopted worldwide to halt overfishing and improve ecosystem outcomes. Rights-based fisheries management generates economic efficiency, and fishers with a financial stake in the fisheries are believed to have the incentive to become ecological stewards. However, the empirical evidence shows no significant impact of catch share adoption on stewardship measures such as use of habitat damaging gears. Based on a wide literature review, including indigenous resource management and modern conservation science, we define stewardship as a measure of ecosystem integrity. Accordingly, we develop a general bioeconomic model that extends the standard property rights model where the market price for transferable quotas equals the optimal shadow value of the resource under catch shares. By modelling the choice of fishing gear, which impacts on ecosystem integrity, as additional control and state variables, respectively, we show analytically how the market price of transferable quotas does not explicitly capture fishing gear effects on ecosystem integrity. Our model highlights the deficiency of catch shares as an ecosystem management tool, motivating an extension to catch share fisheries management such as associated habitat quotas or fishing gear taxes.