there is a way if you don't mind doing a little legwork. Since it is all one image if you tried to use a code it would make the whole image lighter. So to make just the white part lighter you would have to edit the picture with something like gimp or photoshop by cutting out or lightning the areas you want, save it, and then reupload the image. You would then replace the old image with the new one.
you can use this code to replace your pet's image:
{
width: 200px; height: 200px;
background: url(URL)}
just replace URL with the image url, and if the image is a different size, change the size in the code to match.
as for actually getting pet artwork with a transparent background, you can try editing the background out yourself as suggested by , but i find it takes a lot of patience and fiddling to get this to look good. fortunately, sometimes site artists share the full-size pet images with transparent backgrounds, which can be located through this full-size pet image directory organized by .
keep in mind that not all species/color combos have had their full-size images shared, and not all full-size images have transparent backgrounds. it's definitely a good place to start, though.