I'm gonna join the "let it go" committee. For more than one reason. We see little froggies in our yard all the time, we enjoy them- look at them, maybe pet them or hold them for a couple seconds, and then that is it... (we also have cute little lizards, garden snakes, and bunnies- BABY, ADORABLE bunnies currently no bigger than hamsters living in our back yard!). It is really important because it teaches the kids an extremely valuable lesson: Wild animals should remain as such. We should respect nature.
Growing up I found turtles, fawns and baby chipmunks in the woods near my mother's house. The fawn didn't move. I was told that a mother might reject it if they smelled human scent on them. Here I was, 9 or so, standing right next to a cuter-than-words fawn., and didn't touch it. It was hard, but a no brainer none the less... you don't mess with nature. I HAVE, however "helped" injured wild animals by taking them to a rescue center.
The baby bunnies I was referring to were just discovered yesterday in our yard this year. We were expecting them because there were bunnies last spring. Even my almost 3 year old knew to stay away- to admire from afar the little cuties. The frogs we have are really great, too. We like them a lot. Last year I saved four of them from a well in which they were stuck. They must have been trying to get out for a long time because as soon as I got them out they didn't hop away at all.
I'd say admire the little fella. Enjoy him for a day, then put him right back where you found him. Now, if you are insistent on him becoming a member of the family, go to the library and get some books on taking car of frogs, and/or go to your local aquarium/pet store....HOWEVER, this one incident, if you treat it as a "we are letting him go" thing, will REALLY help in the future when a cute turtle or something else shows up. They ask "can we have it?" You could say "remember, they live here, this is their home"- problem solved:)