Current Transformer giving a reading when not clamped around a wire
The secondary of the transformer may pick up some 60Hz signal from the mains even if mains is not actually threaded through it.  The signal would be weaker than if the mains were threaded through the core.  Try moving the mains wire closer and further from the transformer.  If you move it further, the signal should reduce.  You may be picking up the signal from the wiring in the building.

Suppose, you have one of these transformers clamped on a wire W1, while another wire W2 is close by but not going through the transformer.  The transformer may sense both of these wires.  The signal from W1 will be stronger than from W2, though.