Why don't the current readings fall to zero after unplugging the charger?
It is offset and/or noise if it reads when your meter's jaws are closed and not around any wires.

I can't zero my meters lower than 13mA RMS either. Mine is a different type of probe but cannot be zeroed below 13mA RMS at the 10A range. At 100A range it cannot be zeroed below 130mA RMS.

I can zero it so the average is zero, but not the RMS, due to noise (RMS counts anything that strays from zero, whether positive or negative with no cancellation). If you hook it to a scope you can see how much is offset and how much is noise. You can center the middle of the fuzzy line right on the zero of the x-axis and average will read zero but RMS will not due to the fuzziness of the noise.

If it reads only when your meter is clamped around the wire then it is real (or there is a stray magnetic field local to that area so at least the magnetic field is real).