Is purity required to recite the post-prayer Takbir?
Chapter on the Two Eid Prayers
Al-Mughni
Book of Friday Prayer
Primary text
If one commits an act invalidating ablution before reciting the Takbir, one does not recite it, whether intentionally or in forgetfulness, because impurity invalidates the prayer whether committed intentionally or forgetfully, according to our companions (Ashabuna). Ibn Aqil was extreme, stating that if one speaks after the lapse, one does not recite it.
Supporting text
The preferable view is that one should recite the Takbir, as it is an independent remembrance following the Imam's Salaam, and purity is not stipulated for it like other remembrances. Stipulating purity requires either explicit text or meaning, neither of which is present here.