I would have contacted them just to mess with them, like:
"Hi! I have over 20+ years of TV production capability and my crew is very eager to talk to you about this production, as we love kids! What we'll need to start this is an initial equipment retainer of X amount to begin the whole process. Don't worry, we can subtract it out of the 1/3 once filming has begun."
And just make sure X is like the biggest number you can think of