Can a grammatically correct sentence end with the word the?

Yes, a grammatically correct sentence can end with the word "the."

Here are some examples:

* "This is the book I was looking for."

* "The cat sat on the mat."

* "Where is the remote?"

The word "the" is a definite article, and it's perfectly acceptable to end a sentence with an article. The key is to ensure the sentence is complete and makes sense.