extremely rude; most impolite
A strong, formal expression used to condemn behavior as utterly disrespectful or beyond the pale. Often found in written complaints or formal reprimands.
His attitude is extremely rude.
Such a demand is most impolite.
失礼 is a common word for rudeness or saying goodbye; 失礼至極 is a much stronger, formal condemnation.
無礼 also means rudeness but is less formal and less emphatic than 失礼至極.
Compound of 失礼 (rudeness) and 至極 (extremely, utmost). The combination intensifies the meaning to 'the height of rudeness'.