Of the four answers listed, three create idiomatic English phrases: "pathetically grateful", "resiliently grateful", and "mischievously grateful" are all phrase you might hear a native or fluent English speaker say in various circumstances. "Toughly grateful" is not idiomatic, and in fact, the adjective "toughly" is a word that is very rarely used.
The meaning of each of these phrases is as follows.
The person is grateful in a way that makes him "pathetic". A pathetic person is not only a failure, but weak. The dictionary will say that he is "pitiable", but the way we use the word does not imply sympathy, but rather disdain. If someone is pathetic, we ''look down on them''. I hope you can imagine what sort of gratitude would make someone seem pathetic. For example, you could say a strong person who is genuinely grateful for being given pity is pathetic, as strong people should not want pity.
Someone who is resiliently grateful is continuously grateful despite events and circumstances that you would expect would cause him to stop being grateful. For example, let's say Mary saved David's life. David is very grateful to Mary. Mary then proceeds to abuse David, causing him great difficulties in his life. If David is still grateful after the abuse, he is "resiliently grateful". His gratefulness has resilience.
Someone who is mischievously grateful is someone who is thankful, but the thing they are thankful for is something that contributes to their mischief. Perhaps John is playing a trick on Sarah, and asks Robert for a favor to help him unwittingly play the trick. In this circumstance, he would be mischievously grateful towards Robert for the help, especially if Robert doesn't know that this help is going to be a trick on Sarah.
Now, with these three definitions, we need to choose one that fits the sentence. The key word, later in the sentence, is "bothered". His friends "bothered" to read his book. This is not a mischievous situation, so [D] is not an option. The sentence doesn't suggest he is enduring to be grateful over a long period of time-- the tense suggests he is only now starting to be grateful. So only [B] can be the answer. It is pathetic for a man to be grateful at being given a "pity read" of his book.
This is correct and idiomatic.