There are such things as tables for 6 and tables for 8. You booked a table for 6 and are trying to book one for 8 (because you are now 7). If no tables for 8 are available, they only have an obligation to give you a table for 6. If they have a combination of other tables ready, or you are willing to wait, you may get lucky. Just remember they have zero obligation to seat 7 people. They will either say they can seat 6 or you can go elsewhere. They won't put it quite like that but they have the right to deny you.
My advice, keep looking online or find another TS. Otherwise, be prepared when you arrive.