I don't "approach" anybody. I clean up the mess, bill the customer.
NOTHING gets a customers' attention like getting a bill. Much better than negoation.
If the customer complains to me I have three questions for them;
Did the work need done?
Did I do it?
When are you going to pay me?
Don't ever get caught in the middle between other service providers and the customer. Do your job, even if it means cleaning up after someone else. But I'l bet next time they pay a little extra for the tree trimmers to put down protective mats and clean up their own mess.