Noise in DC causing unwanted LC resonance
I had an issue once due to the ground reference being at a slightly different potential at the input to what it was at the opamp. This was due to extremely poor routing of the pcb which introduced an unwanted resistance (Back when we tried to do things 2 layer and ground was more of a weaving spaghetti than what is now just a solid plane). It was a long time ago but I think it was a similar situation where we had a CT that was producing a waveform when there was no current flowing through it. Perhaps have a think about that sort of stuff also.