"We do not need to remember their names."
Translation:Jejich jména si pamatovat nepotřebujeme.
This one is possible. Th former one likely is well, but it sounds somewhat strange. But if you strongly stress "Pamatovat...", it will work as well.
The same sentence will often sound OK or really weird depending on the stress and intonation. And when you ask here "Is this correct?" we have to find out the stress and intonation that it make it to work (well or at least so-so) and it is sometimes not obvious.
Finally, there is only one real answer "Why was it rejected?" for all the sentences in this course. It is because it is not among the accepted translations (yet, perhaps). We do not actively add sentences that should be rejected. We only only add sentences that should be accepted. Often, the reason is simply because it is missing and shall be reported using the "My answer should have been accepted" report button. And then, after some time, hopefully someone will add it. Mind you, it can take some time, even months.