The grip edges for opening the silver razor head cover are located on the inwardly curved sides, i.e. between the razor heads. You would have to lift them on all sides to release the lid from the teeth. However, it works better if you instead carefully lift the lid from the outside on the four diagonal sides where the razor heads are located, then the lid comes off easily.
It sounds tricky, but with a little sensitivity you can do it without breaking it.