How Do I Change a Background Without Cutting Off 'Borderline' Pixels

[Taylor-eOS]

But the pixels don't become semi-transparent of the object color (brown to the left), but semi-transparent in the old background color (white). And if I paint behind that with new background (yellow), I get a border of leftover white pixels from the old background.



The semi-transparent border pixels are not of the object color, but of the background color.