Neighbor asking about having tree cut down

[Jack B.]

Claims it's completely dead and inching toward their house. Tree is on my property. Neighbor has been a constant problem since day one...

1) I doubt that they have a PhD in this stuff and have made exact measurements. I doubt it's moving...There is no evidence of this.

2) I noticed they have two ropes tied to the tree and the ropes go over the fence and their kids play on the ropes...

This neighbor was asked not to park in my driveway repeatedly and I had to call the cops on him to get him to stop doing it. I suspect this is his revenge, trying to pressure me to cut down the tree. 

What would you do? I'm tempted to offer them the opportunity to come on my property and have it cut down at their own expense and they can keep the wood. Either that or ignore them? Every week it's another request with these people...