Grey starts there after Reds fly-half Elton Flatley was suspended for missing a recovery session earlier this week, having stood in for the injured Stephen Larkham for the Wallabies' last two Tests against Ireland and Wales.
Woodward told the official Zurich Premiership website of Grey's inclusion: "Grey is a good player, a very tough player, and it can work in someone's favour by taking the pressure off you, they will probably have him running straight at Wilkinson, and they will probably try and take Wilkinson out that way.
"They will probably be a little more direct with him there, if he is in that position we can put a little more pressure on his kicking game and he is not used to kicking the ball.
"They will probably work players around him that are better kickers of the ball than Grey. It doesn't make much difference though we just concentrate on our own game."
Speaking of any tactical changes against the Wallabies following England's famous 15-13 win against the All Blacks last week, Woodward said: "Evey game you change slightly.
"We did a lot more preparation for the All Blacks because we had been apart for so long, and because we have got all the All Black training behind us it is just a question of fine tuning things, we are just doing a few light training sessions.
"We do change things slightly but nothing dramatically. Its all about concentrating on how you are going to play and you do spot one or two things on the opposition, but we don't go over the top on that, we concentrate on our game and our defence and its seems to be working okay."