Aziraphale isn't really bothered. His own nature makes it a bit hard to be shocked, and his experience in the last year even more so. Perhaps he's more surprised to find, specifically, an ancient Greek god, as the kind he's read so much about - well, after living in the actual culture, of course.
"Oh, quite alright. My apologies, dear boy, I don't mean to make it awkward. Just didn't quite expect to meet the God of Death himself. But I suppose none of us can really escape this sort of thing."
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"Oh, quite alright. My apologies, dear boy, I don't mean to make it awkward. Just didn't quite expect to meet the God of Death himself. But I suppose none of us can really escape this sort of thing."