Open the Find and Replace dialog (usually Ctrl+H). Click More to see advanced options on that dialog. Click Format and then Style. See the first screenshot.
Yes, the screenshots are in Czech. Enjoy :-)
You'll see the Find Style dialog. Choose tw4winExternal style and confirm. Back in the Find and Replace dialog, you will see Style: tw4winExternal under the Find field. See the second screenshot.
Finally, click Replace All. That's it. Word will search for all text marked with tw4winExternal style and replace it with nothing, i.e. it will delete it.