Using Low Gears On Automatic Car Bad For The Engine

We have a Totyota Corolla (can’t remember which year, but in the last 10) and recently the engine has become a bit noisy (few rattles and some purring). My stepdad says it’s because my mother “ruined the car” by using the lower gears to get up the steep hills between my aunt’s house and ours. He says it could damage something called a connecting rod. I have searched and have found nothing to support this, so I was just wondering if any one of you master mechanics could back it up. Anyone ever heard this? Because my mother was taught by her father (who was handy with cars himself) that it was okay to use and even necessary for a little car to negotiate a big hill.
Who’s right? My grandfather or my stepfather? Did my mother really ruin the engine?
Actually I don’t know how old the engine is. We had to put a new (from a pick’n’pull- a lady totalled her car, but the engine was all right) one in it after some mechanic effed up an oil change and the oil leaked out and the engine burned up.
The engine was a few years younger than the original engine, but had the same basic mileage. It was also a Chevrolet engine. Does this make any difference?
She’s overdue for an oil change. She’s been complaining of poor gas mileage as well as the noise, and I’ve told her to get on it. She keeps saying she has to time. I tell her, ‘well, pretty soon you’re also going to have no car.’
From what’s being written here, I think THIS is the source of the problem rather than just her downshifting. She is still killing the car, just not exactly the way we thought. Thanks all. We’re working on her.

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