That'd be the way to do it if you want the images to load faster for your visitors, other than telling the ecom site to get a better server.
You'd want to make sure the ecom site is happy with that, but I don't see why not when it means images are only fetched once (by you) than multiple times by your visitors.
An option would be just to fetch them on-demand, so the first visitor may see them load slowly but further visits would see your quicker loaded image.
More bandwidth on your part but faster images for most visitors. At the very least on Linux there's a simple one line command to delete files that are older than 24 hours or whatever timespan, most likely you'd want to delete them when you know the property listing is gone.