Grammatically incorrect implies the work is factually accurate, but has errors in grammar. Gramatical

is a term used to describe a phrase or word that follows the rules of grammar. To say something is grammatically incorrect would be like saying it is “right wrong” or “correct incorrect”.

What is the meaning of grammatically correct?

"Grammatically correct" means that something (writing or speaking) follows the rules of grammar. For example: He go to the store (incorrect grammar) He goes to the store (grammatically correct)

Why is wrong grammar grammatically incorrect?

It's ungrammatical.

It's 'wrong grammar' because it is used colloquially to avoid a mouthful of words. Grammar is rules/syntax of a language. It can never be wrong. When people says "wrong grammar", what they usually mean is "wrong grammar usage".