I second the statement that to my knowledge also, there is no record of who put something into TC.
In a related note, I can only advise to limit who can use the transport case to a sensible audience, and to not automate the transport.
Take it from me that when I took the system from my predecessor, who had setup an automated nightly transport of the entire TC between test to prod, and someone managed to put all objects (five digit figure) into TC by accident and they got transported, the result was ugly.
I still have not found out how someone managed to accidentally put all objects into the TC, but we have seen a single, odd, "client object" in the TC which we believe resulted from some kind of unintended behaviour, so this scenario might be triggered more easily than one would ordinarily think, at least in the Java UI of V10.