For grayscale (greyscale) JPEGs, Adjust Cover downsamples the image from 256 to 4 colors and outputs a non-greyscale JPEG.
8-bit grayscale images should maintain their colorspace during and after conversion.
Example: Drag attached 1000px 8-bit (256-color) grayscale image into cover art box. Right-click and choose Adjust Cover. Resize to 600px, any quality. Observe unwanted color reduction. Right-click and save the reduced image to a new file. Observe (e.g. in Photoshop) that it's not a grayscale JPEG anymore, and with compression artifacts it now has ~119 colors, but was clearly derived from the 4-color intermediate version.
Output after adjustment in Mp3tag:
Expected output is more like this (made with Photoshop):
