There are a couple of ways to do this.
- You just run the original workspace again, and create a new GeoPackage. Make sure it's set to overwrite, not append, the original file.
- You send only the updated features to a GeoPackage writer, with the mode set to something different. You can use the existing workspace or create a new one to do this.
Here I am using the Update mode. You might want to use the Delete mode instead.
- Do change detection. The advantage here is that it handles updates, deletes, and inserts all in one go. Best to start with a new workspace. Add a reader for the Geodatabase and one for the Geopackage. Connect them both into a ChangeDetector transformer. Send the output to the GeoPackage writer and set the mode (as above) to fme_db_operation
You'll find more detailed instructions for change detection on the FME knowledge base at community.safe.com
Regardless, the Data Inspector tool won't let you edit or delete records. It's purely for viewing data, not editing.