Q: Transmission fluid leaked while pulling a car out of mud

While I was pulling another vehicle out of mud, there was suddenly a lot of smoke coming from under my truck. When I looked under, there was transmission fluid all over. I opened the hood and couldn't find any leaks. The dipstick wasn't showing any fluid however. I noticed that the fluid might have come from a circular seal of some kind, under the truck.There was a small amount of fluid leaked on the ground where the truck was parked. I added some fluid and then a bit more until the dipstick shown full. I drove the truck slowly for a while and checked again. After having seen no leaks, I drove much faster and got home. There were no problems afterwards. I was wondering what that part was that the fluid leaked out of.It looks like a circular metal part with a rubber ring around it. Do you have any idea? Did this damage the truck in any way?