I am a Community College instructor of pre-nursing students. I was taught that "the both" are not words used together. Such as "the both of us" and instead always used "both of us" and left out the. I don't remember exactly which rule this falls under. I have multiple students who use "the both of us" and need to know if this is correct grammar.
We don't use the article with a noun- the both children
We do use it occasionally before a pronoun for added emphasis- I did speak to the both of them . However, in most cases this would sound wrong unless we need to add emphasis, and it tends to be found in colloquial language, at least in the UK. If their use sounds strange, then I would say it is because they are using it when no emphasis is required.