What do you mean by "compress"? On Linux Mint I have an option on the context menu called "Compress..." but that only creates an archive, similar to .zip files. It does not do any image manipulation. Did you not install maybe something else separately?
In any case, I'm pretty sure that you'd have to use some sort of extension for that either way, as I'm not sure something like that exists out of the box. I would recommend looking into this thread to setup the context menu for the images: