That's what keying is about.
I would first open the gif in Photoshop and see what you have really got there. Then when you have removed the background or just enabled transparency, export as a movie from Photoshop with transparency. After Effects sucks at gifs. It's almost always the most inefficient tool for the job.
You can open the images in Photoshop and take out the white background there by clicking double clicking on the layer -> blending modes, and play around with the sliders at the bottom, it's a super fast way to do this. but you may have to do it with every frame..
A gif is a sequence of images, and if those images are imported at JPGs then they definitely won't have a transparent background. PNGs do transparency, JPGs don't. Not sure if that's helpful in your case but something good to know.
Did you solve your transparency issue? Please let us know.