Permanent engine damage would only result from a rather substantial amount of extra oil. How much? Well, more than a quart, more like 4 quarts.
What might happen would be:
1. Excessive oil burning will occur, and this will destroy the catalytic converter.
2. Excessive extra oil will cause the oil in the engine to cavitate (froth or foam), greatly reducing lubricating properties of the oil and causing engine seizure or other internal damage evidenced by signs of oil starvation.
3. Serious oil leaks from various parts of the engine as crankcase pressures build up too high.
So unless the engine exhibited the classic signs of oil starvation, it might be difficult to prove that excess oil damaged the engine.
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