The correct option is
A put off
Phrasal verbs are expressions that involve a verb and another element, usually a preposition or an adverb. The meaning of a phrasal verb is different from the meaning of the individual words.
The underlined word 'postponed' means 'cause or arrange for something to take place at a later time than originally planned', 'delay'.
Option A: 'Put off' is a phrasal verb that means 'to change the time of something so that it happens at a time later than originally scheduled'. It means the same as 'postponed'. Hence, option A is correct.
Option B: 'Put in' means 'interrupt in a conversation or discussion'.
Option C: 'Put up' means 'to let someone stay in your house'.
Option D: 'Put on' means 'to wear a piece of clothing or jewellery'.
These phrases do not mean the same as 'postponed', 'delaying something'.
Hence, options B, C and D are wrong.