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I've followed the instructions above but still have lots of pixels remaining from the previous background colour, how do I remove them?

You posted this in the Gimp 2.8 section but are using Gimp 2.10 There are some differences in use.

The instructions were very simple. Make a selection (of the foreground) -> Invert the selection -> Cut the Selection.

That is ok for a simple image. You need to give more details of the actual type of image you are using.