With the stock firmware, I don't believe there will be a way to do this. A couple of reviews for your router make it sound like that's just the behaviour and there's not much that can be done about it:
You can't control the way the router streams or shares data stored on the connected USB storage device, either. Once plugged in, the entire drive is shared over the network with everybody having full access to it.
The manual does mention an additional utility which may or may not have additional options, although I'm suspicious its entire purposes it to set up drive mappings, not for configuration. I would presume downloaded software would have less settings than the web interface.
USB Print and Storage Manager
The USB Print and Storage Manager helps to manage and monitor the use of your USB printers, scanners, hard drives, and other devices that are connected to your Router’s USB port and shared across your network. USB Print and Storage Manager is found in the Belkin Router Manager icon displayed in your system tray (Windows) or menu bar (Mac).
Now, whether there is anything you can do, I can't say for certain as I don't have this particular router to play with. There are alternate firmwares out there, such as DD-WRT.
I can't see that your router is officially supported, but there is a forum thread about one particular revision of this router. I don't know if it's your one or not as your question doesn't contain this information, but it's a line of investigation you could go down. With DD-WRT, you would have a far greater level of control over what your router does, including how it mounts and shares USB devices information here.
Unfortunately, I can't say how viable this is, it may be a complete dead end, depending on the level of support for your device. I am fairly confident that you won't be able to achieve it with just the stock firmware though, I'm afraid.