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Have you actually tested it with the black background, to make sure that the white outline is showing. Without being able to see the image, I'm guessing that what you're seeing is anti-aliasing. It's usually a half to 1 pixel wide, transparent area around any object. That's how Inkscape and vector graphics create those smooth, clean, crisp lines.
Inkscape's background is transparent by default. So even though it looks white, it's really transparent. Inkscape offers an option to use the traditional checkerboard background, to indicate transparency, if you prefer that. Look in Document Properties > Page tab.
But anyway, if you put it on the black background, and you still see a white strip, please share the file with us, so we can investigate. If you can't share that file, any similar kind of file would be fine. Just trace some other image, using the same settings, and we can still figure it out.