extremely rude; terribly impolite
A strong, formal yojijukugo used to describe or apologize for extreme rudeness. Often used in set phrases like 失礼千万な態度 or 失礼千万で申し訳ありません.
Everyone was appalled by his extremely rude attitude.
失礼千万で申し訳ありませんでした。
I am terribly sorry for my extreme rudeness.
失礼 means 'rudeness' or 'impoliteness' in general, while 失礼千万 intensifies it to 'extremely rude'.
無礼 also means 'rudeness', but 失礼千万 is more emphatic and formal, often used in apologies.
A yojijukugo combining 失礼 (rudeness) and 千万 (ten million, here meaning 'extremely'). The exact historical derivation is uncertain, but it follows a common pattern of intensifying a noun with 千万.