Backing into car in driveway

I would think that this did not cause any strut damage. Strut damage is usually caused when the wheel or suspension is impacted. Unless the suspension or a wheel was impacted I would think that the noise your experiencing is a bent muffler/B pipe. The easiest way to find this out is to have a qualified technician look at the exhaust to look for impact marks, and places where the exhaust is rubbing against the under carriage. If there is nothing wrong with the exhaust then I would move on to try to find the noise in other areas.