You don't delete a highlight from My Clippings. You delete it from the book you added it to. Open the book, select "My Notes and Marks" from the menu, then select the highlight you want to delete, and select Delete. Not sure about the exact interface on the Touch, but it should have something similar to the K3.
The "My Clippings.txt" just contains an extra, human-readable copy of all notes, highlights, bookmarks, etc. It can be deleted, copied to your computer, cut and pasted, etc. The actual highlights, notes, etc. are stored in the .mbp file that accompanies the .azw file for each book.
Thank you, thank you, thank you! Got it deleted from the book. Now where do you go to delete the clip from My Clippings? Or can it not be deleted?