The blurscreen method provided by Garry's Mod (lua) can not be used within the HTML panel at all.
Secondly, the current browser implementation within Garry's Mod is "Awesomium", and is very old, outdated, and buggy. I would be surprised if the CSS3 filters linked by Ballerd work at all in-game.
So, your only other options are to overlay a blur panel on top of the HTML panel (which is likely not what you want, or would be insanely difficult to blur only the parts you wanted), or you'll have to wait until Gmod officially switches to 'Chromium', a separate browser technology. They have an implementation you can play with on a beta branch (search Facepunch for more details), but you'd still have to force all of your players to switch to that branch.