You know it's their fault. You've always known that it is the Time Lord's fault that Clara's dead. It seems that your people thrive to make your life a living hell (quite literally in this case) and the loss of several of your companions is no different.
They don't care who they kill or who they hurt to get to you.
They don't care that they've placed you in this torture chamber to suffer at the hands of your own worst fears and the grotesque veiled creature reeking of rot and swarming with flies. You've been here for billions of years now, caught in this damnable time-loop and stuck burning yourself alive to continue living
How long can I keep doing this, Clara? Burning the old me to make a new one?
And you're angry. No, you're furious, and you're grieving, and this makes you dangerous and unknowable.
Your people want the secret of the Hybrid. And to be perfectly honest (only to yourself, of course) you really don't know who or what that may be but you will never admit that to them aloud. To save Clara means reaching Gallifrey; reaching Gallifrey means not giving into their sadistic game. You watch the wall become thinner and thinner, closer to the Tardis with every repeat performance, and your story goes farther and farther along, and you are heartened by that.
You are heartened by it indeed the deeper you go. When the wall had been smooth and seemingly untouched your musings to the imaginary Clara had been terrified and pitiful. Now there is a noticeable glimmer of hope there for you to physically see and your storytelling becomes more and more frantic and theatrical with each retelling
How many seconds in eternity? The shepherd's boy says—
And little by little you see your escape come closer and closer and your movements become more and more quick and deft. Your tongue is looser but your words are precise and careful.
You're gloating. There's an edge of that in your voice.
The creature behind you burns you again and again, never ceasing in its travel and you burn yourself again and again, never ceasing in your actions until—
Personally I think that's one hell of a bird.
The wall comes crumbling down and you are free.
As you step out of the hell your people have constructed for you, you know already that you have beaten them already. The Time Lords have no inkling of what you are truly aiming for. They tried to make you confess a truth that you barely remember the Sliders telling you about all those years ago.
You have beaten them.
And you always will.