What is the grammatical explanation for using “de” in the following sentence -

“Los niños tienen que dejar de hablar”

See a translation

It has a lot to do with the verb "dejar".
If you say to someone:
"dejar de (verb)"
Dejar de "belongs" to the subject.
But if you say "Dejar" alone, it would be interpretated like they should let something happen

Si no hubiera "de" en esta oración, it would mean that the kids should let someone else talk. But the sentece would be uncomplete. It could be: "Los niños tienen que dejar hablar a su padre" (let their father talk)
But here "de" makes clear that the kids are the ones who are talking, and that they should stop --> dejar. (Something like "leave" that behaviour of their).

This also works with "escuchar" "fallar", "sentir", "ir" and so on

Hope it helps! :)