It has more to do with the noun: niño.
If the direct object of a verb has a "human" referent, then put an "a" in front of it.
And the noun doesn't quite have to be human, but rather, it is personified somewhat by the use of the personal a.
I imagine that its effect is similar to using "who" instead of "what", or "he/she" instead of "it".
Yes, "let in" = "dejar entrar". In this case it does not work, though, "let" = dejar (in the sense of "allow"), the Spanish sentence does not mean they allowed the child in the house, but that the child spent time there, as when you leave a child with someone to take care of it while you work or something similar.
Just double-checking since duo didn't accept my "dropped the boy off" version. Just wanted to make sure it didn't require something else to have that meaning. Also, "They left the boy at my house" could make it seem like they came over to visit and forgot him there. Maybe they wanted "They dropped off the boy at my house" idk
It's "dejaron" and "dejar" not "tejaron...."
Conjugations here: http://www.wordreference.com/conj/EsVerbs.aspx?v=dejar
3rd person plural present tense would be "dejan"