Discovered Check

The rules vary a little (very little) between who is running the tournament.  These rules should be very similar to those of most tournaments however and explain your question:

http://chess.about.com/od/rulesofchess/tp/BasicTournamentRules.htm

and specifically:

http://chess.about.com/od/tipsforbeginners/qt/The-Touch-Move-Rule.htm

which says:

If your opponent makes an illegal move, they must take it back and make a different move. However, thanks to the touch-move rule, if that particular piece can move legally, your opponent still has to move it! For instance, should your opponent try to capture a piece with their queen, only to find out they are in check, they may still have a legal way of blocking the check with their queen....

So anyway the gist of all that is that most tournaments follow touch move and touch move has an impact on illegal moves as well.

In general take-backs are not allowed and ONLY in the case of an observed illegal move are they allowed.  

And the one rule to rule them all: call the TD over and they will resolve the situation.