Greek's on the right track. Do you have the original PSD's of each image?
If you have the original PSD's (presumably with a solid navy background layer),
- In the Layers pallete, click the eye icon next to the navy background layer to hide it. Then you'll get a checkerboard pattern where the navy background used to be.

- Do "File" / "Save for Web..." and for the "Settings" dropdown, select the GIF option with the lowest number of colors that doesn't screw up your image. "GIF 32 Dithered" should probably work fine.
If you don't have the original PSD's and you're just working from the JPEG's that are on the site now, you can still get it to work just fine.
- Open the JPEG
- From the "Layer" menu, select "New >" and "Layer from Background". In the popup dialog, hit OK.
- Press "W" on your keyboard to select the Magic Wand tool
- In the options under the menu bar up top, select the leftmost square icon (it'll say "New Selection" if you hover over it), set the Tolerance to around 30, Anti-aliased off, and Contiguous on.

- Click somewhere on the navy blue background and press the keyboard's Backspace key to delete the background. Repeat in other corners if necessary. The edges may look a little jaggy but should look fine if your page background is similar to the navy background (which it is).
- Do "File" / "Save for Web..." and for the "Settings" dropdown, select the GIF option with the lowest number of colors that doesn't screw up your image. "GIF 32 Dithered" should probably work fine.
Hope this helps!