Just about any site can use any data you provide them for anything regardless of what permission one gives. Asking them to do or not do something has the same effect as asking a mugger to not mug them. At best one would get a chuckle.
The partial exception would be if one has a mutually binding contract with said company and that company is made painfully aware that one has multiple law firms and infinite resources to go after them. They might adhere to the contract for a while until the company gets big and some new middle management want to take risks to look good for their management which means breaking ones contract behind their back.