Have any notable Buddhists commented on Krishnamurti's teachings? Have any important Buddhists made any claim/s about Krishnamurti's teachings? Especially (caveat I know nothing about this) his claim that 


  "Tell them there is nothing to understand"


Bold emphasis is mine.

or


  He claimed that the demand for enlightenment was the only thing
  standing in the way of enlightenment itself, if enlightenment existed
  at all.
I have read a remark by Ajahn Sumedho on Krishnamurti. I don't recall much of the details. But I can tell you that Krishnamurti 's teachings are different from Buddhism, although he has practiced Vipassana himself.
Edit: My answer relates to Jiddu Krishnamurthi, not U. G. Krishnamurthi. I am unfamiliar with U.G.

Sometimes you hear monks or nuns or lay people here saying, 'Don't attach to anything.' So we attach to the view that we shouldn't be attached! 'I'm not going to attach to Ajahn Sumedho; I can learn from anybody. I'm going to leave, just to prove I'm not attached to Venerable Sumedho.' Then you're attaching to the idea that you shouldn't be attached to me, or that you've got to go away to prove that you're not attached – which isn't it at all. That's not being wise, is it? You're just attaching to something else. You may go to Brockwood Park and hear Krishnamurti' and then you think – 'I'm not going to attach to those religious conventions, all that bowing, Buddha images, monks and all that stuff. Krishnamurti says it is all poppycock: &quot;Don't have anything to do with it, all that is useless.&quot; ' So you attach to the view that religious conventions are all useless, and you shouldn't have anything to do with them. But that's also an attachment, isn't it? – attachment to views and opinions – and if you attach to what Krishnamurti says, or you attach to what I say, it's still an attachment.
Ajahn Sumedho
You can be attached to the idea of not being attached. Krishnamurti, for example, would always emphasise not to be attached to anything. He would say, 'Monks, this is all wrong. Religion, monks, all this is wrong. It's not the way.' Then people listening to that would attach to his view, and they weren't aware of the attachment they had to Krishnamurti's view. So the problem is not the view, but the attachment. A view is a view. You can see if you're attached to a view, for or against it. Then the actual practice is to not being attached to any view, and you are very much investigating what's going on.
Ajahn Sumedho

Edit: I added a separate answer on U. G. Krishnamurthi.