Can a time-varying magnetic field pass a metal sheet?
The time-varying field around an AC conductor wire is in the circumferential
direction.   So, it induces current in metal that is perpendicular to that
circumferential direction, i.e. in the radial/Z axis plane.   The current
transformer ought to have no such metal in its shield 'container'.

With a sufficiently low burden resistor, AC performance of transformers can
easily be quite good; that burden resistor and its secondary current
act against the B field penetrating the core, so magnetic core losses
are kept small (because internal B field excursion is small).

As for 'electric field', a good conductor can get quite high induced
current from nearby AC wires, but a good conductor completely blocks
electric field very well: that's why electromagnetic waves (light) 
reflect well from the thin aluminum layer of a common mirror.

Magnetic field does not 'pass through' anything, it is not a flow
of some material.   The field lines are an abstraction for visualization
purposes, not trajectories of particles that can ... bounce.