na-adjective, noun which may take the genitive case particle 'no'
extremely grateful; deeply obliged
Very formal and somewhat stiff expression of deep gratitude, often used in business letters or formal speeches. Conveys a sense of being overwhelmed by the kindness or favor received.
I am extremely grateful for your kindness.
I am deeply obliged by your excessive consideration this time.
恐縮 is a common formal expression of gratitude or apology, while 恐縮至極 is a much stronger and more emphatic version, used in very formal contexts.
感謝 is a general word for gratitude, whereas 恐縮至極 expresses a feeling of being overwhelmed and almost apologetic for the favor received.
Compound of 恐縮 (kyōshuku, 'feeling obliged or apologetic') and 至極 (shigoku, 'extremely'). The combination intensifies the sense of being deeply indebted or grateful.