There is no setting in the web app to remove the border or the shadow.
All you can change is their size and color.
Also keep in mind that light subtitles without border or shadow are only legible on dark backgrounds.
If you want more detailed ways to style subtitles, use either Plex for Windows or Plex HTPC as player apps. Customizing Subtitle appearance in Plex Player for Windows/Mac/Linux and Plex HTPC and PMP
