To remove a person from the staff list of a company, go to the person's record and delete that person's parent. This will remove the person from the company's staff list and remove any benefits that the person may have been receiving because of their relationship or employment with the parent company.
Open the staff person's record
Click into the Parent Member field
Delete the parent from the field (backspace)
Optional: Add the new parent for the person's record
Click the Save button
Learn more about the setting options for who can change an individual's parent company - (1) allow edits from the Member Compass, or (2) lock down to admin-only on the backend.