I was parking my car and I accidentally shifted to reverse while the car was still moving forward slowly. The next thing I heard I was a noise that sounded like grinding, but the car still went into gear. Did I do lasting damage to the transmission? Been thinking about this all day.

 

Most likely you just took down a little of the teeth faces on the transmission gears. You took off a little bit of the life of it, but not really too much. Do not sweat it. But, do not do it too many more times