Deleting already sent texts
I'm assuming you're using Messages on iOS which offers the option to delete your copy of a message. This assumption may not be needed since you can’t delete messages that iOS sends to another device whether it’s SMS / MMS or iCloud delivering it. 

For messages, after a message is sent it doesn't matter what you do it on your side, it doesn't recall or delete the message on the other person's device(s). 

You have the option to delete a text or image in order to save space on your device. You don't control the message content on the other device after you press Send.