Quote 1
"Of course, of course." The Grandma comes a bit closer. (4.419)
This is Jack's first time meeting Ma's mother, and he doesn't yet understand that he can just call her "Grandma" instead of "the Grandma." It takes Jack a while to understand that everyone has a family, not just Ma, and that her family is his family, too.
Quote 2
"For Pete's sake, we're only talking about a minor sunburn and a bee sting," [Grandma] says. "I raised two children, don't give me acceptable standard of care." (5.370)
When Jack transitions from Room to the Clinic, he feels like he's part of the real world. He's still separated from society in a way, though. He's still protected inside the Clinic, but in the real world, everyone gets hurt at some point. Dr. Clay still wants to protect Jack from sunburns and bee stings, but Grandma thinks that's just a way of life. Who is right?