I can't see the top of your page, where you link the stylesheet to your page, but if you are linking with an absolute link (http:// etc. etc.), you are linking to an online file, and that will not be available to be edited locally. I would do as the warning suggests, and download the file to your local system.
If the file is indeed available locally in your site files, then you should change the link to a local, document-relative link instead of an absolute link.
If you are linking to the online stylesheet because it is a standard across departments, then perhaps it should not be edited. You can make an additional, editable stylesheet to go along with (and modify) the styles in the online stylesheet. When you do so, be sure to place the link to your new stylesheet after the link to the online stylesheet.
Open your main Template (.dwt file).
Is your source code referencing an absolute link (http://...) to the style sheet on your remote server? If yes, that's why you cannot edit styles.
Change absolute link to relative link. Save Template. Update child pages.