Many have hired staff they later wished to fire / let go. If they have already been put to work on your settlement, you must go into your staff section and locate them. If you will still have your minimum quota of needed staff then go ahead and dismiss them.
This will bring them back to your ship. Once there, you can go to the upper-right drop down menu in-game and go to the section called ‘View Staff’. Once there, you will see that staff member and may dismiss them. Once dismissed from the ‘View Staff’ page they are gone. You will not need to pay for them any longer.
NOTE: If by dismissing a staff member your quota will drop down below where it needs to be, you must hire another staff member to take this one’s place before you dismiss them, or it will not work.