The kalimba is tuned, so the fundamental for C4 shows as very close to 261.6 Hz. The biggest surprise is that there is no significant harmonic energy, and significant, narrow, stable anharmonic energy between harmonics 6-7. The biggest non-fundamental peak shows up at about 1.714 kHz which is 6.55x the fundamental. This 6.55x component appears in almost all of the notes in the first octave (C4-C5).
I've ruled out interaction with the other keys by manually dampening them while C4 is plucked. What physical mechanism could plausibly be creating this 1.714 kHz peak?