I see the white lines when I view the full size image on a black background (in Chrome).
How are you making the background black? Is it a rectangle with black color fill? If it’s a rectangle the same size as the paper size, try making the rectangle larger than the paper size so that it crops off all edges of the black rectangle when exporting. The white lines might be due to anti-aliasing at the edge of the rectangle.
Does it also happen if you use PNG instead of JPG? Does it show only in the final GIF?
Jpeg is a lossy image format that is designed for photographs where its compression artifacts aren’t usually visible. In images containing large areas of uniform colour it struggles, and results often in ugly noisy artifacts and fringing. That is why I never use Jpeg with SketchUp. PNG is a lossless format that preserves the original pixels and uses a zip-like algorithm for compression.
I was testing this myself the other day as i had the same thought.
Unfortunately PNG doesnt offer much better quality and theres still obvious dithering around edges.
Some photo editing apps have a border trim function (or Crop). Perhaps that would help in this case.
Or exporting a high res image and then running it through a gif converter.
I have to say I see the same sort of thing printing to pdf on a Mac from SketchUp itself. I use the magic wand selection tool in Photoshop to select the background and delete it, but that light pink one pixel line on the border of the image gets in the way, and it takes a few more clicks to get there.