The correct option is B it might rain
In reported speech, the word order and pronouns will be different from
the original speech, because the speaker has changed. Accordingly, the
tense will also change, in most cases.
Normally, while reporting the speech, the tense will change to one tense back in time.
The
direct speech indicates a possibility that is likely to occur in the near future. The speech is reported, hence it will change its tense to simple past.
Option A:
'Might' is the past tense form of 'may' in indirect speech. Hence
'it might rain' is the correct form and A is right.
Option B: 'May' must be changed to past tense as the speech is reported. Hence B is incorrect.
Option C: 'That' in 'that might rain' is repeated twice in the sentence. 'That' replaces 'it' as the subject: 'That that might rain that day'.
As a result, the sentence is incomplete in meaning. Hence C is incorrect.
Option
D: 'It may be rain' changes the meaning of the sentence. 'Rain' does not function as a verb anymore, but as a noun. 'Be' becomes the new verb. Hence D is incorrect.