It's a deterministic process, but it still has inputs. You'd have to know those inputs or test for every possible set of inputs to whatever blurring method was used.

It depends on the blurring method. If you do a gaussian blur, for example, you might be able to do a pretty good inverse blur by finding black frames and performing blind deconvolution. If I were at risk I'd use a nonlinear injective filter instead, to make sure information is lost (linear filtering is not only deterministic but perfectly without noise and no frequency response nulls).

I imagine HBO knows every reviewer they gave a watermarked copy to.