how to update Control Center on my mac

You can use your scanner with Preview or Image Capture. Your scanner will still work fine.

Brother Control Center is a 32-bit application and it will not work in Catalina.

AFAICT there is no update.

If you need a more sophisticated scanning application, try VueScan.

Go to the Brother website and see if they have an update for your scanner.

You could also try to see if Image Capture works with it.