There may be other ways to do it in gimp but this is the way I learned and it works for me.
In paint you are erasing the background in gimp I am masking then separating. I isolate the image with lasso.
Then apply the mask with one click
Then use pencil tool the mask the rest of the unwanted parts.
Here it is completely masked.
Next remove mask.
The you use edit to copy and past as new.
There are a couple more steps the can be applied to clean up the edges but they can be skipped and just save at this point or apply background color.