they let me read this book because it is good. the translation says
ellos me dejan leer ......
the correct answer is ellos me dejaron leer.... because it is in the past
In spanish the past tenses of preterite and imperfect have to do with things that occurred in the past. it is dejaron because the actual action of them allowing you to borrow the book already happened . It would not be has/have/ or had because there are several separate tenses for that.
I know that in Spanish there are different tenses for things that occured in the past. But if I understood the original post correctly, the question was to translate the English sentence "they let me read this book because it is good" into Spanish and with that, the given tense would be the one of the English sentence.
And from that stems my question. For me the sentence could be in the past or present tense as "let" is the same for both tenses. As it is not clearly in the past, at least to me, I would argue that both solutions could be possible (the accepted one and the one from Trevor).