What modality applies to the impossibility of changing the past? Is changing the past logically impossible, metaphysically impossible, or physically impossible?
There are many possible questions here. On one popular reading, to "change" the past (or the future, for that matter) is logically impossible: given that Bob was shot at time t, it is not logically compatible with this to make the world such that Bob was not shot at time t. So we cannot "change" the past in the sense that "first" time t is one way, and "later"(?) that very same moment somehow differs. Change is when one moment differs from another; a moment cannot differ from itself. But this is a trivial kind of 'impossibility'.
At the other extreme, we may refrain from taking any merely contingent facts as 'given', and ask abstractly: is it possible that I perform some action φ, such that Bob isn't (and never was) shot at time t? And that seems possible in almost every sense: there's a physically possible world where I φ and Bob isn't shot. It just isn't this one. (And, more importantly, neither is it accessible in any important sense.)
So the real question must lie somewhere in between. Most plausibly, it depends on some notion of "dynamic" or time-relative physical (causal) possibility. That is, we take the present moment as given, and ask whether we have (sufficient) causal influence over what happens at time t. So the modality of my inability to (now) influence the past is simply a time-relative version of the modality barring me from time travel. 'Physical impossibility given my current circumstances', perhaps?