We can draw, edit, and create animations using GIMP. Layer>Erase background should make the background transparent.GIMP is an open-source raster-based image editor and graphics design tool.Click in a corner of the top layer, this should select the background.Set the tools to the 'By Color' selector.Set Gimp background color from the background color of your image (#eeeeee).This create a new image, you can close the source one. Remove the optimizations: Filters>Animation>Unoptimize. However there is a script that makes this a bit faster if used right: For a single layer, that means Select the background,Select>Grow by two pixels, andColors>Color to Alpha` but this will be long for 68 layers. So the light gray things will remain opaque, and we want to remove the background but prevent Color-to-alpha to change the light gray things into be partially opaque pixels. Export as GIF, don't forget to tick the animation checkbox, and to force all frames to 40ms (the optimization sets a longer interval).This will create a new image, use Filters>Animation>Playback to check it. Image>Interleave layers>Interleave single layer (sprite mode) and select the white layer.Add a layer filled with white (or your new background color).Dark grey can darken to black, but don't panic. Colors>Color to Alpha All layers and remove the background (color-pick, it should be #EEEEEE).Change image to full RGB: Image>Mode>RGB.

Remove the optimizations: Filters>Animation>Unoptimize.But in a GIF, there are no partially opaque pixels, they are fully opaque or fully transparent, so you can't have shadows. In the picture above the shadows would be implemented as partially opaque pixels, that would slightly darken the pixels of the background. When you want a transparent background, you want to be able to show the picture over any background. Then a transparent background is not doable for this particular GIF. It depends if the light gray things are shadows or not.

Gimp gif editor