Hi st87,
Right-click the layer in the Layers panel and select Rasterise then proceed with the selection and deletion of unwanted parts. This is happening because you are probably working with an image layer type (look at the label between parenthesis after the layer's name in the Layers panel).
Image layers are a special layer type that retains all the original image data - you can think of them as embedded images -. They are created when you use the Place Image Tool, the File ▸ Place command or when you simply drag them from the Finder (Mac) or File Explorer (Windows) to the canvas of an opened document. They can be transformed globally (rotated, skewed etc) without losing quality but they cannot be edited/manipulated at a pixel level. For that they must be rasterised first as described above.
