Loop Wave Warp Effect

I know I'm late in the conversation, but I just came accross the same issue and found a very simple solution.

Set the wave speed at 1/(comp length), for example if your comp is 4 seconds long, wave speed should be 1/4, i.e. 0.25.

If you are planning on exporting another gif then you have to set up the comp so that the first frame and the last frame are identical. You can check that with the Snapshot tool. If the GIF you imported is not a seamless look then you'll have to find a frame that matches perfectly then set a marker on that frame. If the gif is seamless then the in point frame will be slightly different than the last frame. It will be the frame before the image is identical.

Once you have that figured out you will need to go to the end of the gif where you marked the identical frames or one frame after the last frame of the gif and adjust your wave warp settings to get them to perfectly match the first frame of the animation.

When you get the first and last frame of your animated layer to match up exactly, step back one frame, set the work area to that frame, trim the comp to the work area, then export the file using the Render Cue and the default Lossless preset in the Output Module. Open the rendered movie in Photoshop and verify all of the motion settings and use Photoshop to export your seamless gif. That's how you make a seamless gif. I can't tell you what settings to use for Wave Warp because you have more than one instance going on and it's too hard to figure out what is doing what at what time.