The small popup which appears before a phone call is called a Caller ID, It searches in a global database (or your contacts) to whom the calling number belongs to. It helps you to identify spammers or unwanted calls.
The screen which appears at the end of a call is called the Aftercall screen. It allows you to interact with the person you just talked to by either sending a SMS, save his number or block him.
But if you don't want it, you can :
1. Skip it when proposed :
2 . You can freely and completely remove it in Settings>CallerID&Afterall>Customise menu by switching off all the options.
When correctly shut down, you should see a yellow bar which indicate the CallerId and the Aftercall are completely turned OFF and won't appear anymore.
3. Go to Settings > Chat options and disable "Display after call infos" or "CallerId & Aftercall" (prior to 2.2m version):
Switch OFF this options.
4. Remove the "Display over other apps" given to Mood Messenger:
Go to Android settings > Applications > Mood > "Display over other apps" and turn it OFF