Since the screwdriver itself was never used as evidence during Maya's/Phoenix's trial, it's possible that it instead was evidence in either Redd White's trial after he confessed to the murder, or April May's trial for wiretapping, with the latter being more likely.
Given that Edgeworth is right in the middle of his Character Development during Case 5, and Case 2 was both his first defeat and the case that planted the seeds for his internal struggle throughout the game, that would explain why he doesn't want to tell Ema about it. Or perhaps it's because he's aware of the Skye sisters' connection to Mia, and Lana's trial wouldn't be the best situation for breaking out the news to Ema (it helps this interpretation that Phoenix himself only told Ema that Mia "no longer works here", albeit that might have been more of a case of him still grieving somewhat, since he didn't know of their connection yet).
