Remnants left when deleting background using foregorund select

[Brimfulof]

This seems like it should be a standard use, so I'm sure this is just a setting I'm missing, but I can't figure this out. Any suggestions appreciated.
I have a group of photos of people taken against a blue background (although it's not completely uniform). I want to remove the backgrounds, so I just have the images as cutouts.
I've used the foregorund select tool to create a selection around the person, but whatever I do to then delete the background, some remnants of the blue remain. These are outside of the selection line, so I'm not sure why they are not deleted. Images below illustrate what I mean.
What I have tried:

1. Foreground select (based on Compound colours).
   
2. Remove holes.
   
3. Cut the selection.
   
4. Paste to new layer.
   
5. Delete old layer.
   

Also:

1. Foreground select (based on Compound colours).
   
2. Invert the selection.
   
3. Remove holes.
   
4. Add alpha channel to the layer.
   
5. Delete the (inverted) selection.
   

Selection created - line is where I want it to be.





Selection created - line is where I want it to be.



Selection inverted and deleted - remnants remain inside the (inverted) selection line.