bucket fill right to the edge?

[Ofnuts]

1) remove the current color with color-to-alpha. If necessary, make a fuzzy selection on the background and and grow it by one or two pixels so that it covers the edge pixels. Off-white pixels will be partially transparent
2) bucket-fill with the new color (using the same selection) using the bucket-fill tool in Behind mode. This will complement the partiall transparent pixels with the new color

The Gimp fill tool is advanced enough once you have read the doc