I don't believe that certain criminals should be eligible for reduced sentences, no matter what kind of good deeds they do. There are some people that simply need to fulfill their debts to society and serve their entire sentence. For simpler crimes, I can see where certain things could be a good way to reduce one's sentence.
A good deed does not minimize the harm and damage an inmate caused by his crime. However, a good deed does show that he is making progress in respecting laws and that should be rewarded. An inmate's sentence is tied to the nature of his crime, so that should not be reduced. Instead, he should get rewards such as more leisure time or family visits.
No, if a person is punished for some crime by an imprisonment, then there should be no mercy. If he could commit a crime, he can endure the sentence, as simple as that. No manipulations of this kind should be allowed. I think that any convict can manipulate the guards and pretend he is good, but don't forget what he has done in the first place.
It is nice when an inmate can earn a reduced sentence by doing a good deed. However, it is not practical to always hand out reduced prison terms to inmates that do good deeds. The reward should be based on what the inmate's conviction was, what their likelihood for rehabilitation is and what the good deed was.