I think one has to distinguish here between "lembrar" and "lembrar-se". In this particular sentence imho the correct meaning is that the mother was reminded of something, as it is suggested by DL. If it were "her voice reminded me of my mother" (using the reflexive verb form) the sentence would look different, as preacherbob pointed out; but that's just not the practice sentence here.
I believe you are confusing the reflexive use of the pronoun "me" with the (in)direct object pronoun "me". To be reflexive the subject and object must be the same but here the subject is "A voz dela".
I was able to discuss this sentence with a native speaker of Brazilian Portuguese and it appears your instinct about the meaning is correct. The problem is that both the original sentence and the translation don't scan very well. This can be fixed by the addition of a few words, for example "A voz dela lembrava a minha mãe de um papagaio" makes the "Her voice reminded my mother" (in this case of a parrot) interpretation quite clear.
On the other hand the minimum change required to make the sentence meaningful is the addition of "me": "A voz dela me lembrava minha mãe" which means "Her voice reminded me of my mother". Another possibility is adding "a da" to get "A voz dela lembrava a da minha mãe" which is roughly "Her voice resembled my mother's".
"A voz dela lembrava a da minha mãe" would be, "her voice reminded me of that of my mother" / "her voice reminded me of my mother's voice"? But being reminded of one's mother's voice and being reminded of one's mother are related but different sensations.
As anyone who's lost or is far from or is not in contact with one's mother can probably attest, sometimes you hear a voice and think, "wow, she sounds s lot like my mother," and other times, you have an actual memory of your mother, triggered by someone's voice. Very different things.
When I saw the sentence in its simplicity, (without any additional pronoun or conjunction) I thought it was a beautiful, endearing idiomatic expression. I came here to the forum to say that, but it looks like everyone is saying Duolingo has it wrong? If so that's disappointing.