Normally you can plug in and unplug an EHD from a 6131. It has to reboot as the EPG (electronic program guide) is stored on the 6131 when no drive is connected, and on the EHD when it is.
I don't know how you may get your Jets games back, but if I may suggest, try another EHD first to see if it is the 6131 that is the issue rather than the EHD. Maybe, put your 2TB away for awhile, someone may come up with a fix.
Do you own any other 6131's?
If Life is a Highway,...then why is there no end to this dirtroad?