The driver package may have been shared with other installed printers, or the uninstaller left the service behind. Use the Brother Cleaning Tool from their official website.
If you no longer use the Brother printer:
The utility periodically checks for newer driver versions or firmware updates. Depending on your settings, it may notify you when an update is available or automatically download minor patches. This is especially valuable for network printers where drivers can become out-of-sync with the print server.