Semantically, I don't hear any real difference in meaning. The difference is one of tone or attitude. One thing to bear in mind is that #2 with "should" sounds dated and oddly formal to my ears. I'm a US English speaker. That said, #2 technically speaking sounds more like the speaker is talking about a hypothetical. It still suggests that she indeed said "such a thing", but the emphasis is more on the fact that even hypothetically it would be surprising. One might say this if, for example, what "she" said is especially surprising coming from this person because of her personality or otherwise some particular reason. #1 is a more common way of expressing essentially the same idea at #2 except without the implied hypothetical stuff. Its meaning is simpler and more direct. It's the way a speaker would most commonly express this idea.

Like a previous teacher mentioned the should doesn’t really add to the surprised feeling as it has already been stated she is surprised in the first statement, so the should is redundant in that context. You could add WOULD as it adds an imagining feel as to say I am surprised that she would…..

Since the speaker says that he is surprised, it follows that he is surprised. Both sentences are natural. You can also say "would". Few native speakers would detect any difference in meaning here between "should" and "would", although there is a difference if one wants to be picky. However, #2 (with either should or would) is definitely different from #1.