How to remove wire from insert connector in recessed light fixture
If you were to detach the connector from the group retainer by releasing the tabs you might find a wire release tab or slot on the connector. Otherwise...

Try twisting the wire as you pull. Sometimes they'll sort of screw out with a bit of effort. Remove the damaged portion of the wire and re-strip before using it elsewhere.

Cut the wire and re-strip it. Leave a stub on the connector to which you could reconnect later, or which you can cap or tape to insulate the exposed wire. (You could also just loop it back into the same connector to secure and insulate it.)