According to Larousse, Collins and Academie-françiase, « serre-tête » is invariable. Word Reference and Robert list «serre-têtes», but it is not the 'official version' apparently.
SERRE-TÊTE. n. m.■ Ruban ou coiffe dont on se serre la tête. Des serre-tête.
Freeform Writing Exercise B1
Thank you for pointing this out, it has now been corrected.
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