The reason why Charlie tells his story to Parker is because he can tell that she is the “Charlie” character in the love story of her and Hardison.
She’s the one who can take care of herself. She doesn’t dream, she plans. She even has a way with languages (see: “you speak Spanish?” *shrug*)
Hardison is the one who’s like Dorothy. He’s the loyal one. He’s the one who’s always finding homes for the team. He’s the one who waited.
So the reason Charlie tells his story to Parker - the reason he tells her to “not waste time” - is because he sees himself in her. He can tell when someone’s found their home, their family, and he knows that she shouldn’t let that go.