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The blue background is still visible when you view the image using PSP. But open the image in your browser and presto...that awful blue is gone!
Here are a few additional tricks that will help you make flawless transparent GIFs.
Round-shaped objects have jagged edges when you create them using 16 or 256 colors mode.
You can create smoother, anti-aliased edges in 16 million colors mode. But anti-aliased edges make it harder for you to isolate all of the background color. There are usually a few pixels around the edges that are a slightly different color than the one set to be transparent. It is very hard to get rid of these pixels without disturbing the smooth edges.
The solution is to plan ahead. If you know the color of your web page, use a similar color for the background of your graphic.
The stray pixels are still there, but now they blend into the web page's background.

Sneaky, but effective.