The point is whether there's something contained in Sheila's bible reading of which Jeremy could claim to have no knowledge but which would implicate her in the crime. Remember he claimed to Julie that this was the "perfect crime", so no trail leading to him, no forensic evidence, him gambling that he had done enough to rope her in as an accessory should she disclose, which makes me think he didn't care much for her in the first place, that she was a mere expedient in the whole process.