T-trades have nothing to do with shorting, they are simply a trade or a number of trades an MM didn't report during market hours. FINRA only requires them to be reported on the same day they happened.
T-trades are likely many of the shares used to cover MM's naked shorting. T-trades are large blocks, or part of a large block of shares being sold by insiders and toxic lenders. The MM's don't print those trade real time because the MM is trying to keep the PPS from tanking more than it naturally is. T-trades are those blocks being printed to the tape EOD at an average price of those trades done throughout the day...