You start with "I noticed you teaching Susie (insert concern here) when she was taught to do it this way and she's kind of uncomfortable doing it your way".
No, the parents have no role or say in strategy and I say that as a parent.
Is it "strategy", or individual technique? An example of "strategy" is where to go with the ball in a given situation, over which the coach absolutely has the final word. If it's individual pitching or hitting technique, there might be room for discussion. A good coach doesn't demand a player change a clearly effective individual technique, even if it's not what they would have taught.