Final answer:
The correct answer to fill in the blank is D. help, which completes the sentence as 'They offered us help' or 'They offered help to us'.
Step-by-step explanation:
The correct answer to the question 'They offered __ us' is D. help. In English grammar, the verb 'offer' is typically followed by a direct object without needing a preposition or an infinitive when the next word is a noun. Therefore, the correct sentence would be 'They offered help to us', or more commonly 'They offered us help'.
The other options, such as helping (A), for helping (B), and to help (C) would require a different sentence structure or the use of 'offer' as an infinitive verb phrase, which is not the case in this sentence.