Yes! To turn off your Rewards emails you just need to locate your Rewards settings. Go to the Profile Menu and select Settings from the drop down menu.
There you will see several tabs including Rewards. You can update any of your Rewards settings on this page. If you scroll to the bottom you'll see a simple toggle that says "Send Rewards Emails".
If the toggle is purple (as shown above) then that ability is on and your customers will automatically receive emails with updates about their Rewards progress. If it is grey then your customers will not receive any automatic updates on their Rewards progress.