They are run by the comptroller general who is appointed by the president meaning that the president has total control over who gets paid anything at all. Right now ours is just an "Acting Comptroller General" filling in until the president appoints someone else.
https://www.law.cornell.edu/uscode/text/31/702
>> (a)The Government Accountability Office is an instrumentality of the United States Government independent of the executive departments.
The law establishing it also establishes it as independent.