What?
Which one is ugly?
How can it have a transparent background and a white background?
I'm going to go out on a limb and try to guess what you're talking about (although my track record for mind-reading is not very good). There's a very thin gap between each object, so that if you put a white background behind it, looks like a thin white line between objects. If you put a red object behind it, it would look like a thin red line. Is that it?
First, at the size of the original objects, that gap will probably not show up. So you probably don't need to do anything. Try putting it at 100% zoom and find out. I mean they look like approx 16 x 16 px icons. I can't see the gap at their original size.
Second, the easiest way to get rid of it will be to add a stroke to each object, which is the same color as each object (black stroke for black pieces, gray stroke for gray pieces, etc.).
Third, the best way to get rid of it is to manually edit each and every piece. By nodes, using the Node tool, make objects underlap each other. Don't move the objects, but move the nodes.
If that's not what you meant, please try again to explain it