Pitcher Entering the Game

 
In the middle of an inning, the defensive coach replaces his starting pitcher. During the relief pitcher's 8 warm-up pitches, the relief pitcher is throwing very poorly. After 6 of the 8 warm-up pitches, the defensive coach starts to replace the relief pitcher with yet another pitcher. The coach of the offense likes what he see in the original relief pitcher and reminds the umpire "that a substitute pitcher shall pitch to at least one batter, or until a third out has been made".
 
What does the umpire do now?
 
Call
In NF, an unannounced substitute does not officially enter the game until he takes his position AND the ball is made live (NF 3-1-1). In the situation below, the first relief pitcher need not pitch. Another pitcher may enter and pitch.

Another way to remember this rule is to note that if a player goes out behind the plate to warm up his pitcher between innings (while the catcher in the line-up puts on his catcher's gear), we do not consider that warm-up catcher to be a replacement for the actual catcher.