Hi Jill

It looks like the Learning Plan completion comes through as a Totara Alert.

It is possible to turn off email alerts for an individual by selecting preferences in their profile and Notification preferences and Email for online and offline to Off.

This will turn off email notifications for all alerts though so probably needs to be turned back on. There may be other Learning Plan notifications that could come through too so may not be that practical to do. 

What is required is a feature request to have finer control over messages which is what the centralised notifications is aimed at doing in the future.

Regards