The dreaded "Fringe"
This is a GIF issue...JPEGs don't show transparency.
When a GIF graphic has a transparent background,
the Anti-aliased edges bring along remnants of the color of the original background.
In the examples below, Photoshop's Save for Web was used to set different matte colors
in the Optimizer window.
This example used a white matte.
This example used this page's blue background as a
This example used the "none" matte option.
Notice how the none option produces no anti-aliasing on the
outside edge of the graphic.
This never shows a fringe, but it is always ragged.