Block text messages - here but not there. Help

Up until yesterday, I was able to block text messages from various people on my iPhone but still have them show up on my Macbook. I loved this option - work people could not bother me at all hours but I wouldn't miss their messages when I opened my computer. I don't know if a recent update eliminated this feature or if I simply did something to stop it.

Anyone have any insight to help me get this feature? I am connected to iMessage.