So putting a faraday cage like thing in your hat would protect from this, if we believe it, right? So all the CIA needs to do is have a standard issue hat. Lined with the right stuff. Tinfoil is probably the right thing for many reasons.
A faraday cage must be enclosed metal all around. A hat has a big hole where the head goes :) I don't think it will function as one. Microwaves are very prone to bouncing.
It should significantly reduce the signal strength though.
