na-adjective
extremely rude; outrageous; utterly insolent
Strongly emphatic, often used in formal or written contexts to condemn behavior as beyond the pale. Combines 不届き (improper, rude) with 至極 (extremely).
彼の不届き至極な態度には、さすがに私も怒りを覚えた。
Even I felt anger at his utterly outrageous attitude.
役所の不届き至極な対応に、住民から苦情が相次いだ。
Residents complained one after another about the municipal office's extremely insolent response.
Compound of 不届き (improper, rude) and 至極 (extremely). The exact historical derivation is uncertain, but the combination serves as an emphatic formal expression.