I have a theory.
First, you need to understand that GIF files are indexed. This means, each pixel is a reference to an entry in a color table, which in turn is simply a set of up to 256 RGB values. (Pic related, this is the color table for
>>18621229 viewed in a GIF editor.)
What this means is that when you edit an entry in the color table, -every- pixel of that color will change. So, my guess is that the GIFs were recorded from the Pokedex, then someone went in and manually looked for the color distortions caused by the polka-dot overlay and changed them to the proper value. Voila, it's like it was never there. All that's left is to optimize the file to get rid of the duplicate entries.
Because the models use cel shading and very little antialiasing, this process shouldn't take more than a minute per GIF. Again, this is just a theory.
