Actually, it is possible, but it would take a lot of work on your part.
The code involved would be this:
Code:
a[href="neomessages.phtml?type=send&recipient=dolphinling"]{background-image:url(somebackgroundimage);}
a[href="neomessages.phtml?type=send&recipient=dolphinling"] img{visibility:hidden;}
The first line selects only the link that points to your mail, and sets a backgound image on it. You'd have to make this background image yourself, and host it somewhere. The second line makes the actual image invisible so you can see the background. The link will still work normally.
You would have to also do this for every other image you wanted to make transparent, changing the urls--that's why it would be a lot of work.
The reason you have to do this is twofold: First, Internet Explorer doesn't support semi-transparent pngs. Web developers have griped at microsoft about this for ages, and it'll finally be put in IE7, which will come out who-knows-when. Firefox has supported semi-transparent PNGs since day 1 (as has Safari, and Opera has for a long time).
The other part of the reason is that Neopets doesn't like using transparent gifs. They have a good reason for that: the edges of transparent gifs are jaggedy, and not nice to look at. So they give them a white background, and that's what you see.
For reference, the "filter" code that you were using is Microsoft's answer to not having semi-transparent PNGs. The thing is, it's more work, harder to use, and can't do nearly as much.
If anyone wants to see why semi-transparent pngs are nice, look at
my userlookup and scroll around in both IE and Firefox.