I've been looking for an app like this, so I decided to give it a try.
Found out that if you have a contact on the Springboard and you want to remove it from the SB, open up Call Me, go to the contact you want to delete, press the red - sign, and push delete. It will ask you if you want to delete contact, and you want to click yes. This doesn't remove the contact from your contact list, it removes it from your SB. You contact should still be in the Call Me list. This worked for me, so if you need to, try restarting your phone or removing the application and reinstalling it.
One bug I found is that if you click No instead of Yes, neither the red - or the green + show up for that contact anymore. Just restart the app to fix this. It's still version 0.7, so there will be some bugs.
Hope this helps!