Por que a tinta se comportou dessa maneira em Hell Bent?

Claro que é simbólico. Também faz sentido, dado o que sabemos sobre os personagens.

The graffiti is in remembrance of Clara.  The mundane world probably thinks of Clara as missing, but Rigsby knows that she is dead.  He decorates the TARDIS as a memorial, since he's the only one left behind who knows he has something to remember. 

At this point, the Doctor also remembers Clara, but he wasn't left behind.  He was trapped for uncounted billions of years before he could even try to rescue her.  He survived those aeons and did attempt to rescue her.  During those aeons, he refused to leave her behind. During that attempt, things change. 

Part of the rescue attempt would involve making Clara forget about the Doctor.  She is unwilling to lose those memories, even at the cost of her own life.  She sabotages the memory-altering device.  Knowing the sabotaged device was unpredictable, the two agree to use it.  As a result, instead of Clara forgetting the Doctor, the Doctor ends up forgetting Clara. 

The Doctor is aware that he's forgotten something.  He spends time talking to a stranger (who happens, unknown to him, to be Clara herself) while he tries to decide whether to chase the missing memories or simply leave the forgotten person behind.  In the end, we suspect he decides to leave the lost memories unexplored. 

Ele não diz isso em voz alta. Ele simplesmente pula em sua TARDIS e desaparece.

O TARDIS é um personagem. Ela é sensível, inteligente, mentalmente conectada e emocionalmente ligada ao nosso amado protagonista. Ela é capaz de pensar e agir em seu próprio interesse e nos interesses dela.

Prior to this moment, the TARDIS preserved the mementos.  If the Doctor had decided to chase these memories, the TARDIS would likely have continued to preserve them.  Why not?  It's easy enough for her to keep them inside her integrity field. 

Of course that she doesn't is symbolic.  We've seen Clara escape the end of her own story several times.  The writers had to give the audience some signal that says "her story is over -- and we really mean it this time".  From a Doylist perspective, the symbolism is unavoidable. 

The reason that it works is that the TARDIS is a character.  The Watsonian perspective makes sense.  When we see that the mementos are left behind, we understand that the TARDIS agrees with the Doctor.  Maybe the Doctor leaves Clara behind by accident, but the TARDIS leaves her behind on purpose.  She is supporting his decision.  Because the graffiti is left behind, the audience understands that from the TARDIS's perspective Clara's story has (finally) ended. 

The TARDIS leaves behind mementos of someone that she agrees that the Doctor shouldn't try to remember.  Before that, she kept them around because she hadn't made up her mind or even considered the question.  The only explanation I need is that the TARDIS is doing, at each moment, what she feels is best. 

Aviso: especulação.

A TARDIS do Doutor não precisa se desmaterializar para chegar lá. Se Clara já tivesse materializado "ela" TARDIS em torno dele, ela poderia tê-lo trazido e separado do Doutor por uma parede interior na cena do restaurante. Quando ela mais tarde desmaterializou a dela, deixando o médico para trás, ela também poderia ter deixado sua TARDIS. Somente quando a TARDIS do Doutor se desmaterializou, desta vez sob seu próprio poder, a tinta caiu.

Naturalmente, isso ainda é inconsistente com alguns outros exemplos de coisas que ficam do lado de fora da TARDIS enquanto estava em vôo. Jack Harkness pegou uma carona assim uma vez, e houve um caso em que a TARDIS estava coberta de panfletos, que pegaram fogo, mas continuaram ligados. Então, novamente, a continuidade inter-episódios de Stephen Moffat sempre foi, na melhor das hipóteses, irregular.