How Do I Leave A Group Chat In Messages For iOS?
Open the group text / chat you would like to leave on your iOS device. Starting in iOS 8 you will find a Details button in the top right corner of the screen. Tap Details, swipe all the way down to the bottom, then choose the option that says "Leave This Conversation".
If the option is greyed out for you or doesn't appear, it means that not all users are using iMessage. Unfortunately, this new feature only works if all participants are using iMessage.