Pitcher's Substitution Rules after Pick-Off

With one out and the bases loaded, the starting pitcher (P1) is replaced with a relief pitcher (P2). With a 3-0 count to the first batter that P2 faces, P2 picks off the runner at first base for the second out of the inning.
 
Which of the follow are true (excluding any injury to P2):
A) P2 can now be replaced with another pitcher since P2 recorded an out
B) P2 must remain in the game until the third out of the inning is recorded
C) P2 must stay in the game until the current batter (the one with the 3-0 count) completes his at-bat (retired or reaches base)
D) None of the above
 
Call
A substitute pitcher must pitch to the batter then at bat. With the exception of an injury, the substitute pitcher must pitch to that batter until the batter is retired, reaches first base, or the third out is made (NF 3-1-2).
 
In the question below, "A", "B", and "C" are not true -- so the answer is "D".