D seems right to me.

there isn't much ____ requires a noun here, and "taking care of them" is playing a noun here.

The correct answer is A. When we say that there isn’t much to something, we mean that it is easy because it does not include many responsibilities, duties, skills, etc.

I am still confused. Why the answer is TO TAKING?
There isn't much to taking care of them?
Is there any grammar which is" to +V_ing "in this sentence?

The other options are ungrammatical and do not make sense. To + verb-ing occurs when the object of a preposition (to) takes a gerund (or gerund phrase, in this case) as its object.

To me, the question and the answers are not well conceived. Don't feel bad if you are feeling confused.
Maybe this can help you see better.
Thank you for taking care of Butch while I was away.
There wasn't much to taking care of Butch; he is a good dog.

This is similar to " I am looking forward to travelling around the world after I retire..". Or, she is g

thanks so much

sorry. But i had a class this afternoon. And my English teacher said the correct answer was D. taking because it had to be a noun to fill the gap. But you told me the correct one was A.
I don't know who is right and who is wrong. Can you check and explain to me again?

If your teacher says D is the correct answer, then he is probably not a native speaker of English. I would find a new teacher.

Yes, he is not a native speaker. But he teaches English at my school. And he insists on his way of thinking on this matter.
I think i have to tell him about that. But how can i tell?

You don’t have to tell him anything. What counts is that you know how to say it correctly.