TARDIS is a trans dimensional being who experiences everything at the same time. It's why she has such favorites among those who travel inside her.
The Doctor, her thief, will always be the most important one to her, he was mad enough to be stolen after all, but out of the strays that he brings along, she will always treasure some above others and one above all else. Just like her thief would, after meeting her.
Rose Tyler. Bad Wolf. The girl who kept coming back. Would always come back. Her Heart.
Sometimes, when she is feeling particularly melancholy, she will play some of the happier footage of Rose: when she accepts the invitation to join the Doctor, when the Doctor calls her beautiful for the first time, when they rescue her from the Daleks, when they saves the Doctor from the Daleks, when she accepts the new regeneration, et cetera to the end of her first stay in the TARDIS. She doesn't dare to view the footage from the second time Rose made (will make, has made, one or the other) the TARDIS her home.
The Doctor sometimes catches her at it and she can always feel his confusion over the woman on her screen but she doesn't feel the need to elaborate. Other times it's the strays who catch her viewing it but then she closes the files and doesn't bring them up for anyone, no matter how much they plead. If they ask the Doctor, he most likely replies that because the TARDIS is a trans dimensional being who views the whole of time and space at the same time, the woman could easily be someone from his future, the TARDIS' past or someone else entirely. When they look at him with blank faces, he'll elaborate "It's all timey-wimey and spacey-wacey."
When she is trapped inside a frail human body, talking to her thief for the first and only time, they do end up talking about the strays.
"Wouldn't it be amazing if we could always talk, even when you're stuck inside the box?" he asks, with a delighted smiled on his young face.
"You know I'm not constructed that way," she answers seriously. "I exist across all space and time and you talk and run around and bring home strays! And the one stray I love, you send her away when she was ready and able to give you forever! Give us forever!" Then she falls because one of the human body's kidneys has failed.
They make it back to her shell, her body, her home, and to the control room after a few clever words from her thief and she's released from the human body, erasing the House from her control matrix. For the last time, she takes on the look of her Heart, her golden hair falling on her shoulders, radiating golden light.
"Doctor," she says in a breathy voice, her accent matching that of Rose's cockney. "Are ya there? 'S so very dark in 'ere."
"I'm here," he chokes out. "Why her?"
"She looked into me an' I looked into 'er," she answers. "She's my 'eart, forever." She pauses. "I've been lookin' for a word. A big, complicated word but so sad. I've found it now."
"What word?" he asks softly.
"Alive," she answers just as softly. "I'm alive."
"Alive isn't sad," her thief shakes his head minutely.
"It's sad when it's over. I'll always be 'ere but this is when we talked an' now even tha' 'as come ter an end," she said, looking her thief in the eyes. "There's somethin' I didn't get ter say."
"Goodbye," her thief whispers.
"No," she says back. "I jus' wanted ter say, 'ello. 'Ello Doctor. 'S so very, very nice ter meet ya."
"Please," her thief begs. "I don't want you to."
She just smiled, not Rose's tongue-through-teeth smile, but her own, gentle smile. "My wolf and I, we both love ya," she says as she fades back into her control matrix.
Later, her thief is putting a firewall around her matrix when the pretty one and the orange one try to talk to him.
"How's it going under there?" the pretty one asks.
"I'm just putting a firewall around her matrix. I'm almost done," her thief says, and the pretty one walks down the stairs.
"Are you gonna make her talk again?" the orange one asks.
"Can't," her thief answers, the longing already buried deep inside him.
"It's spacey-wacey, isn't it?"
"Well actually it's because of the-" her thief began the techno-babble that nearly no one was smart enough to follow, except himself and the Doctor Donna that once was (is, will be). When the pretty one tried to connect two wires her thief agreed that it was indeed spacey-wacey.
"Sorry," the pretty one apologizes. "At the end, she was talking, she kept repeating two things. I don't know what she meant."
"What did she say?"
"The only water in the forest is the river and that her heart will return when the thief howls," the pretty one repeats dutifully. "She said we'd need to know that some day. It doesn't make sense, does it?"
"Not yet and not anymore," agrees her thief. "You okay?"
"No," the pretty one sighs. "I watched her die. I shouldn't let it get to me but it still does. I'm a nurse."
"Don't let it get to you. You know, that's called being alive, best thing there is," her thief grins at his strays. "Being alive right now is all that counts." He sits back to the swing. "Nearly finished! Two more minutes and we're off! The Eye of Orion is restful, if you like restful. I never really get the hang of restful. What do you think, dear? Huh? Where should we take the kids this time?"
"Look at you pair," the orange one chuckles, leaning on the railing of the stairs. "It's always you and her, isn't it, long after the rest of us are gone. Boy in his box off to see the universe."
"You say that as if it's a bad thing but honestly, it's the best thing there is," her thief smiled at his strays. "Ehh… the House deleted all the bedrooms, I should pull you two a new one. You'd like that wouldn't you?"
"Okay, um, this time, could you lose the bunk beds," the orange one asks.
"No, bunk beds are cool!" her thief argues. "A bed with a ladder! You can't beat that!"
The pretty one slaps his forehead with the palm of his hand and sighs.
Her thief pouts. "It's your room, up those stairs, keep walking till you find it," he says and gestures to the stairs above himself. "Off you pop."
"Doctor, who was that second woman, the blond one?" the orange one asks, not leaving.
Her thief looks at the orange one. "Her name's Rose and she's the reason I continue to do this, saving the world and universe and multiverse, because somewhere across time and space, she's still running, her hand clasped in mine, be it in stone age or the year five billion and twenty-three on New Earth."
"Where is she now then?"
"Trapped in a parallel universe. With a clone of me. He's human, he can give her what I can't. They even have a TARDIS so he can give her the stars again, along with pink and yellow and brown children."
The TARDIS wants to tell her thief that while their wolf is indeed in a parallel world where she cannot go, their wolf will come back one day, when he needs her the most, long after the pretty one and the orange one have gone. The strays always think they're the one to stay forever but only their wolf can and will give them forever.