To clarify some of the speculation in this thread:
The warble, or distortion, that occurs with a tonal input to the hearing aid is most likely the result of an interaction between that tonal sound and the feedback cancellation algorithm.
This warbling distortion is often called entrainment. The sound can be heard by anyone listening to the hearing aids. Many sounds will cause entrainment, door bells, some voices, and music.
A hearing aid is more likely to entrain when the system is close to feedback. This means that higher gain fittings that are not well occcluded are at greater risk for entrainment. Moving to a more occluded fitting or reducing gain will reduce the extent of entrainment, it’s unlikely that this will completely eliminate it.
How to get rid of entrainment:
Most of today’s hearing aids offer different feedback canceller settings. Moving the settings from fast to slow, or adaptive to static, or high to low should all reduce the extent of entrainment. Turning the feedback canceller off should eliminate the problem (not the preferred option).
Why does this happen:
In short, the hearing aid thinks that the tonal input is a form of feedback. The feedback canceller identifies the tonal sound and attacks it. Because this is not true feedback distortion results.
Today’s feedback cancellers:
All of today’s leading feedback cancellers use phase (sound) cancellation. Please note that the phase cancellation is far more robust than simply adding a phase inverted copy of the whistle. This is what makes today’s hearing aid fittings (comparatively) stable and allows for an impressive range of open fittings. A second layer of feedback management is gain restriction. At least one company uses gain restriction that occurs dynamically during wear and most use gain restrictions that are placed (and remain fixed) at the time of fitting.