Alan will pick a curtain. If it contains the car, great -- his turn is over. (He can look at another curtain if he is curious, but cannot communicate what is there to Becky.)
If the first curtain he opens does not contain the car, he may try one more. If he fails, game's over.
The curtains are then all closed and Becky comes out, after Alan is removed. Becky picks a curtain. If it contains the keys, they are winners. If it doesn't, she has one more chance to pick the curtain with the keys.
If they pick at random, Alan has a 2/3 chance of finding the car and Becky has a 2/3 chance of finding the keys. so they have a 4/9 chance of winning.
If they can improve their odds, it is only through their selections, not heel scuffs on the floor, chalk marks on the curtains, etc.