Do they need to know how Caylee died ??? for a conviction
No...not legally.
Nope.
No. Not in a circumstantial case. It is the sum total of all the incriminating evidence that clinches a circumstantial case.
As an example...Dr. Bierenbaum killed his wife in his NYC apartment. Cut her into pieces. Put them in duffle bags. Drove to the airport...put her remains in his private plane. Flew out over the Atlantic Ocean. Dumped her remains which were never found. He was convicted of murder without the prosecution ever proving the exact method of her death—strangulation? Maybe.
The doc was convicted and is still in jail.
There are many other cases where a body was never recovered and exact manner of death never proven where the perps were convicted by the efforts of a shrewd prosecutor meticulously building a circumstantial case block by block, piece by exquisite piece to convince a jury.