She used to disparage her neighbor every now and then.

The correct answer is D. denigrate.

To denigrate is to speak about someone or something in a very negative way. It is a form of criticism that is often unfair or unjustified. In the context of the question, the woman is speaking about her neighbor in a very negative way, which suggests that she is denigrating her.

The other options are not correct because they do not accurately describe the woman’s actions. To please someone is to make them happy or satisfied. To praise someone is to express admiration or approval of them. To belittle someone is to make them seem unimportant or insignificant.

In conclusion, the correct answer is D. denigrate.