It's not up to you: insurers have the legal right (called "subrogation") to seek reimbursement of any amounts they paid out from someone else who is at fault in causing the injury and therefore the insurer's payment. The insurer does not have to simply absorb the loss, but can get the money from someone who was legally in the wrong in causing the expense. So if you have received money from one of your insurers, they are allowed to go after the neighbors if they feel that they are or may be at fault, to recover any and all amounts they had to pay out due to the accident.