Quick follow-up.
The whistle made it impossible to sit in the tub and relax while the circulation pump was running. Sorta like after the main jets stop, just sit and relax. There was not relaxing with that whistle. Did some more investigation today. It is obviously that screen/grid in the intake hole under the circulation pump filter. It does not look like it can be removed, or I was too scared to break it. In the end, I took a tiny bit of waterproof grease I use on my softener and put it on that grid in a few places. That seemed to eliminate the sound. I am pretty sure there must be a hairline crack in that grid, but no chance I can see it. Odd they have the screen in the one filter intake, but not the other - it is just a gaping hole.
Whatever the cause, at least it seems the waterproof grease has silenced the whistle.