In Barrie's play, it transpired that Little Mary was in fact 'the stomach'. The conceit was that one could change one's life by what one ate.
This is a strange theme for a play and we can imagine that some people, especially sensitive people like Miss Marple, were shocked by this literary device.
Once members of the audience learnt that Little Mary was 'the stomach', they hardly knew where to look. In other words, they felt awkward.
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