IIRC Zahra's mattress that was removed from the house was brand new. Either LE wanted to find it to determine if it was trashed because there was key evidence on it and/or to confirm the story of the Baker's that it was simply updated.
LE searched where it was said to be dumped and did not find it so, that either denies the Baker's innocent mattress upgrade story or implies it does contain key evidence -- or both.
could it be possible this mattress was dumped at the previous place they lived, before the moved to the current location...if so perhaps they need to check the dump site of where that garbage would be at in the landfill