Parents always worry about their children being led astray by unsuitable friends.
Is this sentence grammatically correct? What is the grammar of "their children being led astray"?
This is correct.
"Being led astray" is a preposition-gerund clause that modifies the sentence "Parents always worry about their children." Preposition-gerunds add more meaning to an already complete sentence.
All about Gerunds: https://www.englishpage.com/gerunds/part_1.htm)
Examples of Gerund-Preposition clauses: https://www.grammar-quizzes.com/gerund3c.html)