Sending accidental texts

When I accidentally touch a text thread for too long, optional messages to send pop up and I keep accidentally sending out texts (or my cat walking across my phone does!). How can I turn off that "okay" "talk later" option? It's annoying. I had been trying to swipe up to get it to go away and that would just send the last option. You have to CAREFULLY tap at the top to get it to go away without sending something. I've tried everything in settings for keyboard, assistive touch, 3D touch etc.......nothing is making it go away and my friends iphone doesn't do it, so I know it's possible. Mine is a 6s.