The real answer is to avoid this situation.
The proper way to remove the design is not to do a plain fuzzy-select + delete (or color-select + delete), When you do so, the pixels on your design that are on the white-to-black transition (and are various levels of gray) are either cut out or left in (and those left in make that white halo). And no, there is no proper threshold setting, if it is too high you get a pixellated/jagged edge, and if too low you get the white halo, and in the middle you get both.
The proper way is to do a color erasure:
- fuzzy select the part of the design you want to remove (white, I would guess)
Select > Grow by a couple of pixels
- Set the bucket-fill to
Color Erase mode
- Bucket fill the selection with the color you want to remove (white, I would guess)
When you do this, the pixels that are completely white are made totally transparent, and those on the white-to-black transition are replaced by black with various levels of opacity, that are composited cleanly with the pixels of the background layer and make a nice smooth edge.
See here for some more details.
PS: Come to think of it, you shouldn't even have to do this. The design should have been made on a transparent background (and possibly as several layers)...