IMO, I don't think she did. When MS confessed to her that TB was "gone, gone" he also confessed that it wasn't the first time he killed and burned a body. I think that's likely when she maybe put it together, and that's what she subsequently told LE. Unfortunately, it wasn't admissible in court, for reasons I have yet to understand.
I can see how it would be prejudicial. They're not on trial for burning any body, they're on trial for burning a specific body. There is no evidence that the body MS referred to was LB's, so there would be no factual basis for a jury to associate his statement with Laura, but there is certainly a danger that they would.