In itself, it's not capable of increasing your import from the grid. If you're moving it and the reading is changing, that's to be expected (to an extent) because whilst CTs are pretty good, they are not as accurate as direct measurement.
What it does is convert a fluctuating magnetic field into a voltage that represents the current flowing in the cable it is clamped around.
It works because the magnetic field strength is proportional to the current flowing in the conductor and the voltage from the CT (which is essentially a coil of wire) is proportional to the field strength. So, higher voltage = higher current. Moving it will alter the field strength and thus it may appear to increase or decrease the current it is reading. The reality is it's not changing it, it's just exagerating the inaccuracy inherent in this measurement method.