How can Batman run and climb in the pits without his knee brace?

IMHO, I think Bruce Wayne was still wearing his knee brace. We never saw his knee to confirm that Bane took it off.

We just assumed that Bane took it off, because it seems logical. However, think about it from Bane's perspective:

Bane was talking about breaking Batman. He said that he would break his body and soul. He did break his back leaving him crippled. All was left is to break his soul.

He was so sure that Bruce wouldn't even try to fight back or come after him (Remember his surprise when he saw him again).
A man so sure of his victory won't bother by simple details as a knee brace (which is neither a weapon or a communication device) when your opponent is already half dead and prisoned in a pit he himself failed to escape (again remember when he was fighting batman and bragged about being born in the shadows contrarily to batman who training in shadows ).