Tire size difference tolerance AWD?

1 tire on my 2010 limited was recently damaged beyond repair, The tires it has are the (20") Michelin LTX premier, with 7/32nds tread remaining, from what I can find, these tires new are 9/32nds deep. I know that AWD vehicles should have all 4 tires matching, what I am wondering is how much tolerance there is with this? Would I risk damaging drivetrain with 2/32nd difference? (I don't want to damage anything, but I also don't want to splurge on a full set of new 20" tires if not necessary.