This piece is called an "engine mount isolator/dynamic damper" by Subaru. It hangs from the front crossmember/transmission cradle. It appears to be a sort of mass damper. We have noticed this can sometimes get damaged or go missing during transmission installs.
Fits all 2002-2007 Subaru Impreza/WRX/STI, plus 2005-2009 Legacy and Outback.