I've uploaded several transparent background PNGs to my site and I actually link to them, and it is important to maintain the transparency for the image. I still wanted to have a white background for when people open the thumbnail, though.
I found out a really simple CSS edit. Simply go here:
Find this segment:
And replace the background with whatever color you want. This will allow you to keep the transparency on your image, but make it easier to view on the website. Hope this helps some.