That tree appears to have been vary much alive. Did it fall as a result of the storms? If it was alive, the claim will be made on their homeowners policy, and their decutible will apply. As a general rule, most insurance providers allow up to $500.00 beyond the decutible amount for the tree removal. In other words, if the home was damaged and repairs are needed, they will have to pay they decutible and once that's satisfied, their incurance policy will probably cover up to $500 to have the tree removed. Do you by chance know who they are insured with?