The Department of Homeland Security is a cabinet-level arm of the Executive Branch. The Sec'y of Homeland Security directly "runs" that branch, and serves at the pleasure of the President of the United States. There is a House committee on Homeland Security which conducts "oversight" and handles legislation related to security. There is likewise a Senate committee. This is the DHS page on aviation security; and this is a house report on TSA oversight, connected to this bill which did not become law, but is on the topic as an example of what legislative oversight would mean.