So you think the WordPress built in Gallery shortcode is actually pretty good, but you can't get rid of that irritating grey border around the images,  here's how:

.gallery a img { border: 0 !important; }

The importance of the being !important; No need for fancy filters, or plugins.  Just add the above code to your own stylesheet.  The !important function means that this style overrides any later css, like inline styling (that is not itself also "!important").

Update: if your images are not links, you can remove the "a" selector.