I've recorded two clips with the cell phone. One with bass guitar through Axe-Fx (just In1 -> Out1), the other with the Synth block (one voice, sine wave, some freq. between 100 and 200 Hz). I think it's especially noticeable with the sine wave, as the distortion changes with the volume. It sounds like a filter opening/closing, emphasizing overtones. Given it's a sine wave, I guess overtones should be absent or very weak, so I attribute them to the distortion.
I played several notes on the bass and switched through frequencies to rule out any resonances of the speaker/cabinet.
I've attached a zip file with the two m4a files if anyone is interested.
I hope Thomann will understand the issue and can make sure they don't send me another one.
On the upside: I tried it on Tuesday in rehearsal and was very pleased, although I didn't tweak any patches and could not focus on the sound. Just plugged in and played with the band (and the candidate for the vacant drummer position).
That said, older patches I tweaked on my FBT 12ma sounded quite different, not in a good way. Patches I created from scratch at home (with near fields) translated well and sounded quite nice. So I'd like to have this monitor but without the distortion

It's not noticeable in rehearsal room though, with the increased volume and everyone else playing and talking. I did not do the synth block test though.
Now contacting Thomann.