GMAT grammar book query

'say' here refers to what Peter said. The intention here is that you actually heard Peter say "I am going out with Becky tonight", but you haven't specified the person to whom he was saying.
'Tell' should be followed by 'to whom you are telling'.
Since no noun comes after the blank here, we should use 'say'

We usually follow 'tell' with a personal object (the person that we are speaking to). We usually use 'say' without a personal object:
She told me that she loved John.
She said that she loved John.
He told everybody that he had to leave.
He said that he had to leave.

Notice how 'told' is sandwiched between the speaker and the listener in above examples, while 'said' doesn't need to be followed by any object.

See this link for more details :
https://www.englishclub.com/vocabulary/cw-say-tell.htm