Well, if the council sent me a letter telling me to pick up leaves from their tree as they're a danger hazard, I'd definitely write to them and ask them to remove the source of the problem, the tree.
I'd send them a letter to remove their tree!
Failing that, chop it down yourself and plant a new one (is that allowed?) if you're supposed to maintain the nature strip, I cant see why it wouldn't be if it's a safety issue and they wont do it.