From the app:

1. Go to the "My ShowMes" section of the app and find your ShowMe.
2. In the top right corner of your ShowMe tap the gear that opens ShowMe settings.
3. To delete or unpost it, select “Remove”. To make it private, tap "Private". (Note that Premium Membership is required for this)

From web:

To take down your ShowMe, visit www.ShowMe.com and login from the top right corner. Thereafter, hover over your name to make a menu appear. Select "Edit ShowMes" and from the next screen you can delete your ShowMes or make them private.(Note that Premium Membership is required for this)

Making a ShowMe private will allow you to still see it on the web and share it but only those with the direct link can view it.