Well, you "can" run with differing versions, but sometimes there are oddball issues that come up. The farther away from matched they are, the more likely the issues will arise. I sure wouldn't update the TIU to 6.1 and leave the remote at 4.xx, that will very likely cause you issues somewhere down the road.
In order to check the version of the TIU, you go into the SYSTEM menu and scroll down to TIU SETUP, then scroll to TIU VERSION and press the thumbwheel. Obviously, it helps a lot if the TIU is powered on and configured to talk to the remote. 
