Unfortunately, by trying to "put it right" or "make up for their supposed mistakes" or whatever we call it, your parents were probably doing exactly what many post offices were doing. Fiddling the figures. Not in the sense of stealing money, obviously - in fact, the exact opposite - but essentially, falsifying their figures to make the cash in the till balance with the computer figures.
Suppose (for the sake of argument) that this computer system gave random wrong figures for 100 post offices a day, leading to the postmasters being unable to reconcile the till. Most of these would be for trivial amounts - say, less than a fiver. "Not worth wasting all evening sorting it out", so the postmasters would open their wallets and make the cash balance to the computer. Or take out the extra few pounds from the till and bung it in the float jar that we all know they have, and nobody can admit to having... the system encouraged this, by calling it "careless money handling" or "fraud" every time a postmaster told them the till didn't balance to the penny.
The Post Office didn't know about these. They only knew about the discrepancies that were so large that the postmasters couldn't hide them. And because they didn't know about the small ones, or the "overs", they seem to have assumed that ALL the discrepancies were large cash shortages. They don't know the scale of the problem, even now; I mean, the number of discrepances that actually occurred, including the ones where the staff made up the difference, or that were too small to worry about.
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Cesario, the Count's gentleman
