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).
Even I felt anger at his utterly outrageous attitude.
Residents complained one after another about the municipal office's extremely insolent response.
不届き alone means 'rude' or 'improper'; 不届き至極 is a much stronger, formal condemnation.
至極 is an adverb meaning 'extremely'; here it intensifies 不届き to form a set phrase.
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.