I'd agree with it coming through the mike cable. Just added this electret fist mic from Amazon to mine (??) which doesn't appear to have a shielded cable. This LCD screen became corrupted on speech peaks and sometimes locked in TX which didn't happen with an electret element soldered directly to a mic plug. I'm running an end fed half wave on 20m but there's an RF choke on the coax just before it enters the shack which should block any RF, never-the-less RF was getting in through because as soon as I put a 22nF cap across the PTT and ground pins on the back of the mic socket it cured it. I seem to remember this being pretty standard practice even on CB's and the like.
M0WWS