Robert, I'm sorry, but this is like saying Joel Quenneville uses the fact that he used to coach for the Blues 15 years ago as motivation when the Hawks play them now. I doubt that that gives them any extra motivation, same with Florida. Gallant has been with how many different organizations since the Jackets? A lot. He probably doesn't even know anybody in the organization anymore.
I don't think the players wanted to win this one for Gallant any more than they did the other times they played the Jackets this year. This is a stupid argument. If anything, they were motivated more by being in the playoff race than some silly thing like you're suggesting.