Hull City's McGregor missed the Scots' two friendly games with the United States and Norway because of a thigh injury.
In his absence, Cardiff's Marshall has recorded two clean sheets and Strachan said: "I've known David for a long time and he's now got a presence about him that he didn't always have.
"It's not arrogance, it's just a self-confidence. He hasn't changed off the pitch. He's still a very quiet and unassuming man but there is now a presence on the pitch.
"Is he now putting Allan McGregor under pressure for the number one spot? Yeah, I think he is.
"I'm enjoying working with the lads and the longer it has gone on the more pleased I've been, especially after a poor start.
"That start affects people and tests your mentality. But it's good to be here picking up another victory. That keeps us going for another three and a bit months until the next game.
"I look back to the Wales game (2-1 home defeat) and that was a long night. I'm getting better sleeps now."
Don't forget you can watch David Marshall in action for Cardiff City when they take on Manchester United on Sunday 24 November at 16.00