A user needs to restrict users from editing the mapping and settings of a saved CSV import that they have shared.
Ensure that the Allow Audience to Edit checkbox is unmarked.
This checkbox can be found when going to the Setup > Import/Export > Saved CSV Imports > Access column, then Shared.
As per Field Level Help, "Check this box to allow users with whom you have shared the import map to edit it, meaning they can make changes to it and save it with its same name. If you do not check this box, and users modify the import map, they can only use the Save As command to save it with a different name."