Hey Dale,
Do the below steps help? I tested this out in 15.2 and 15.4, and after using these steps, it removed the fields from my new UX Timesheets, but let me know if there is still anywhere you still see them.
1. Go into Classic UI->Administration->Project Management->Timesheet Options.
2. Move Input Type Code and Charge Code from Selected Columns to Available Columns and Save, then these should be removed from the timesheets.
Thanks,
Kristin