The circuit is most sensitive to alternating magnetic fields with a frequency harmonically related to the oscillator frequency. Screens of Al or preferably tinplate are effective. It is preferable to make them with >6 cm clearance from the ends of the board. If they are closer and can physically move, they can couple to the sensor field and give a false reading. I checked the overall frequency response of the sensor by fixing a single 1" square of thick copper wire to the shaft of a miniature electric motor. I mounted the loop about an inch from the outer end of one sensor coil and varied the rotational rate of the motor to modulate the magnetic field.
The simplest way to check for interference is to wedge the ferrite rod armature and check that the output signal is constant. The only interference source that I experienced was due to the computer monitor several feet from the sensor. Trimming the oscillator frequency removed the problem, additional screening was a bonus. This sensitivity is only a problem if you don't know about it.