Pretérito perfeito composto do subjuntivo
"Nós não acreditamos que ela tenha feito isso."
We do not believe that she had done that.
The subjunctive is used to express doubt in Portuguese. "We do not believe" expresses doubt.
If there were no doubt, it would be:
Nós acreditamos que ela fez isso.
These are tempos compostos of verbs. In English translation, they are verb with auxiliaries, basically. [ter feito, have done, tinha feito, had done]. In this case, in Portuguese, there is the added difficulty of the subjunctive, which does not carry over into the English.
This one is used like this:
Here is a full description of them: tempos verbais compostos
"Uso dos tempos compostos do subjuntivo Pretérito perfeito composto do subjuntivo:
Indica uma ação que já está concluída e que é anterior a outra. Exemplo: Ninguém imagina que eu tenha visto seu irmão."
Please note: Where it says that one action is finished and comes before another, that is contextual and not given in the actual sentence. So, it's something like:
"Ninguém imagina que eu tenha visto seu irmão [antes de que ele foi embora]."
No one imagines I had seen your brother [before he left.]
The subjunctive there is also there for the "doubt factor" of the verb to imagine in Portuguese. Compare that to:
Ninguém pensa que eu tinha visto seu irmão [antes de que ele foi embora].
Both are translated as had seen in English.
In English, it's basically the same thing regarding an earlier action. We use past perfect when another action has taken place or is implied.
I am taking this next explanation from this text: Pretérito mais que perfeito You can see the conjugations in the text.
The pretérito mais que perfeito is not much used in spoken language. It corresponds to past perfect in English.
- Quando o noivo apareceu, a noiva já chegara na igreja.
What is used in spoken language, is the form with the auxiliary (tempo composto). Also, past perfect in English.
Quando o novio apareceu, a noiva já tinha chegado na igreja.
The pretérito mais que perfeito thus is either formal (chegara, for example, in the third person singular) or in spoken language ter + the past participle (ter chegado). In some cases, haver + the past participle.