All sorts of ways, Sometime in the past the white with a feathered edge as been merged with the background. You really need to keep that feathering otherwise a hard edge looks awful.
My suggestion
1. You can use the paint tool as an eraser. Set the mode to colour erase, use a large-ish brush, white FG
2. Now make a selection of the part to colour change. Enable the alpha lock in the layers dialogue and then fill.
3. You can invert the selction and fill the other half or whatever you want, paint in / gradient all sorts. Turn the alpha lock / paint tool mode off when finished or you will forget about them and it will come back to haunt you.
4 . Add a white layer under and merge down if required.
Some screeshots of all that. https://i.imgur.com/uiWRg6q.jpg
Other ways ? You can use rotate colours for the purple to green but not that easy to specify an exact green example: https://i.imgur.com/w5lKNXP.jpg
My suggestion
1. You can use the paint tool as an eraser. Set the mode to colour erase, use a large-ish brush, white FG
2. Now make a selection of the part to colour change. Enable the alpha lock in the layers dialogue and then fill.
3. You can invert the selction and fill the other half or whatever you want, paint in / gradient all sorts. Turn the alpha lock / paint tool mode off when finished or you will forget about them and it will come back to haunt you.
4 . Add a white layer under and merge down if required.
Some screeshots of all that. https://i.imgur.com/uiWRg6q.jpg
Other ways ? You can use rotate colours for the purple to green but not that easy to specify an exact green example: https://i.imgur.com/w5lKNXP.jpg