Try if it disappears if you change GPU Preview to CPU Preview (Cmd E or Ctrl E)
If it disappears it is caused by anti-aliasing and you can prevent it when exporting to an image by using Art Optimized anti-alliasing.
Use vectors in the pattern maker, if your logo is an image, vectorize it first without background.
When creating the pattern, make sure you don't have fractional pixels in the Width and Heighth boxes in the Pattern maker. I started with a black version to get the position right and saved a copy with a white version.
I filled a rectangle with the white version, rotated it 45 degrees and added an second black fill in the Appearance panel.