For annotations on maps:
If the lines are seemingly random in nature, and aren't a SIGMET or AIRMET, then they are most likely Map Annotations.
They can take the form of different colours or even text. Usually, they are used for reminding yourself to take certain actions at a certain point. i.e. to change to a particular frequency at a certain distance point along your flight path.
These annotations are automatically shared amongst your iOS devices that are logged into the same AvPlan Username.
To clear them, take the following four steps:
They will automatically be cleared from your other devices too (as long as they are connected to data).
For annotations on plates: