Yes, Gordon, I was thinking the same way, some small relay with normally opened contacts.
The thing is, if LCD is in unknown state, resetting Arduino will not help, you need to reset backpack, and the only way to do is by switching of it's power.
What's interesting - it's like there is some way of resetting backpack by some command, because when in "garbaged state" a couple of times I managed to reset it (initiate splash-screen) sending out some x7E combinations, but it never worked next time 
So I think there are some undocumented backpack commands that may invoke reboot.