I don't know about Continentals, but I do know Lycoming requires a teardown inspection for a prop strike. A friend of mine hit a deer (sounds very similar to your incident) and Lycoming, when asked, was very clear that the prop hitting anything while under power was a prop strike.
Personally, even without knowing this, after an incident like that a couple things go through my mind.
1. You are not in a good mental state to fly. Get a room, sleep it off, and take another look in the morning. You'll live through a flight school chewing your ass. You probably won't when you have a low altitude engine failure at night.
2. I would not fly a plane after something like that without an A&P recertifying the plane as airworthy (in writing in the logbook). If it was a quick inspection like what you saw, I'd ask to see the manufacturers procedure for the inspection (even if I don't have a clue what some or most of the mx terms are). It will keep the A&P honest and you may very well learn something as they explain the inspection to you...
My $0.02 worth. Like anything in aviation, there are a million ways to skin a cat, and each pilot is dead set that their way is the best!