Yes. You will need to edit the feature layer settings:
1. Open the details page of the hosted feature layer you are using in Field Maps
2. Click on Settings>Scroll to "Feature Layer Hosted"
3. Under "What kind of editing is allowed" untick Add
Thanks for the quick reply Jovana, that works but unfortunately we still need them to be able to add, they are just copying attributes from a service that is in the map - not collecting points at a new location.