Replying to myself: I looked at the schematic for the CloudBit and perused the design manual and app notes for the i.MX233 SoC. I think there’s a flaw in the circuit design. Here’s my hypothesis:
The design uses the headphone output on the MX233 to generate the continuous signal - this in and of itself it good and creative. The problem is in the signal conditioning chain. The first op-amp circuit references the signal to the ground-plane and not to the headphone reference on the SoC. The consequence is the ground bounce that occurs because of network traffic (that radio in the wifi dongle draws alot of current!) gets amplified by the output circuit and shows up on the CloudBit output. This could be avoided by wiring the reference “ground” to the headphone “ground” pin on the SoC.
This could be tested with a jumper wire, but I’m not skilled enough to hand solder that fine pitch QFP!