First of all, I don't think it is a good idea to make these borders invisible, since you then won't know what or if an album is currently selected.
But if you still want to do that:
First check if the skin you are using is an xml or an xmlc skin.
If it's xml, you will need to learn some skinning. (find the elements I mention below, and change their values)
If it's xmlc, create a new text file, paste the following text into it, replace 'OriginalSkin' with the name of the skin you are currently using and want altered, and save the text file with a name of your choosing giving it the xml extension.
So something like "NoBorderSkin.xml"
<?xml version="1.0" encoding="utf-8"?>
<root dependsOn="OriginalSkin.xmlc">
<element id="Content[Artwork].Body.Highlight" bg="255,255,255" />
<element id="Content[Artwork].Body.Lowlight" bg="255,255,255" />
</root>
This will create clear white borders. If needed, read the link I gave you earlier for more clarification.