I still don't think the audio IC should be cleared so easily, or the filtering, just because an IC can mute like it's supposed to. I also suspect the counter, they can make noise also, in fact they often do, but when working correctly it's negligible and largely unnoticed.
Try unplugging the power cord from the wall, turn the radio ON to drain away any residual, then unplug the white counter plug on the right side of the counter. Don't fiddle with it while it's powered, you can damage the input to the counter. Plug the radio power back into the wall and check for noise.
If noise is still present, do the same steps above except put back the white connector on the right of the counter and remove the rear power connector from the counter, check for noise.
If noise is still present, the counter isn't the source, restore all connections and start looking at the audio chain.
A clip of the noise would be very helpful.