A gas turbine membrane seal is disclosed. The gas turbine membrane seal includes a membrane, the membrane configured and arranged to extend from a first gas turbine component to a second gas turbine component and to separate two volumes, and an anti-fretting part configured and arranged to be attached to the first gas turbine component. A face of the anti-fretting part is adjacent to the membrane, and the face of the anti-fretting part is convex. Further embodiments of the gas turbine membrane seal are also described, along with a gas turbine having the gas turbine membrane seal and a retrofitting method.