Are "Bad Wolf" signs permanent and fixed Spacetime entities?

Question

When Rose Tyler possessed the Time Vortex, she brought Jack Harkness back to life — and because she didn't have control over it, Jack Harkness became immortal.

From The Sound of Drums episode transcript:

JACK [OC]: Last thing I remember, back when I was mortal, I was facing three Daleks. Death by extermination. And then I came back to life.

[Radiation chamber]

JACK: What happened?
DOCTOR [behind door]: Rose.

[Yana's laboratory]

JACK [OC]: I thought you'd sent her back home.
DOCTOR [OC]: She came back. Opened the heart of the Tardis and absorbed the time vortex itself.
JACK [OC]: What does that mean, exactly? (Yana is crying.)
DOCTOR [OC]: No one's ever mean to have that power.

[Radiation chamber]

DOCTOR [behind door]: If a Time Lord did that, he'd become a god. A vengeful god. But she was human.
(Flashback to Parting of the Ways, Floor 500 of the satellite.)
ROSE: I bring life.
(Jack remembers his first coming back to life.)
DOCTOR [behind door]: Everything she did was so human. She brought you back to life but she couldn't control it. She brought you back forever. That's something, I suppose. The final act of the Time War was life.

But, she also created "Bad Wolf" signs across time and space. Are those signs also indestructible just like Jack Harkness? Is there a reference to back this up?

Answer 1

The Bad Wolf is a meme that got spread through time and space. Hints about it are dropped throughout the season. The Bad Wolf Tyler implanted the meme in multiple people to point the way to the Doctor and her earlier self. Very Timey Whimey.

The End of the World:

DOCTOR: A Repeated Meme is just an idea. And that's all they are, an idea.

Boom Town:

ROSE: What's it mean?
DOCTOR: Bad Wolf.
ROSE: But I've heard that before. Bad Wolf. I've heard that lots of times.
DOCTOR: Everywhere we go. Two words following us. Bad Wolf.
ROSE: How can they be following us?
DOCTOR: Nah, just a coincidence. Like hearing a word on the radio then hearing it all day.

Bad Wolf is found on multiple things. The Bomb in The Doctor Dances, which explodes. The chalk drawing in the Powell Estate was still there, faded, after 9 died and 10 was born. The graffiti that 9 made the kid clean up. During Turn Left the Tardis is covered in Bad Wolf signs where the regular Pull to Open sign is, but in the next scene at the start of The Stolen Earth, the Bad Wolf signs are gone and it's back to normal.

As they are all subtle background references, there is nothing to suggest they are or are not fixed points in time.

Answer 2

The "Bad Wolf" messages can be erased or otherwise destroyed, as shown when the Doctor makes the kid who painted "Bad Wolf" on the side of his TARDIS clean it off in "World War Three", and it has not ever returned. This is because what Rose did with Jack was different from what she did with the words; with the words, she simply scattered them across time and space so that they would manifest in various ways along her own timeline. Whereas with Jack, she was explicitly trying to bring him back to life and got carried away with the power of the Time Vortex when doing so, resulting in his immortality.