If I understood your question correctly, do the following:
1. Click on 'person' icon in top menu having clicked 'close' to top left of 'Load List'
2. Click on your profile name at top
3. Click on "Local Logs" in "User Logs" list
4. Slide all the way to bottom of your "Local Logs"
5. You should then see three choices: "Send All", "Delete All" & "Mail fieldnotes.txt" ... click on "Delete All" and all the local logs are deleted
I follow this regularly when I haven't send the local logs to geocaching.com
Hope this helps