The Nuvi 3790T does not allow for user data editing or deleting from within BaseCamp, only adding. To delete items on the your nuvi please do so on the device itself.
The SD card operates in the same manner as the nuvi. It is only possible to add new data not edit or delete.
When you say that you deleted the data on the nuvi did you only delete the gpx file or did you use the UI of the device? (Where to=>Favorites then the context menu). Editing the actual GPX files is not recommended.