Special Counsel Independence and Integrity Act This bill sets forth requirements and limitations with respect to the removal from office of a special counsel appointed by the Attorney General, or of another official appointed by the Attorney General who exercises a similar degree of independence from the Department of Justice (DOJ) chain of command. Specifically, a special counsel or other appointed official may only be removed by the Attorney General or the most senior Senate-confirmed DOJ official, in certain circumstances; may only be removed for misconduct, dereliction of duty, incapacity, conflict of interest, or other good cause; must be provided written notice that specifies the reason for removal; and may file an action to challenge the removal not later than 10 days after notice was provided.