Is it correct to report in box 8 an unqualified student's grant income? It was not part of original w-2 from the employer.

Do you mean Box 8 on a W-2? No, you cannot alter a W-2, it must be entered the way it was reported. 

If the student received an education grant that is not listed on a tax form, you would enter that in the Education Section under Deductions & Credits.

Act as if you want to enter a 1098-T (but don't) until you get a screen for adding additional education aid. 

You need to clarify your question.  For example are you asking about how to report employer educational assistance? What do you mean by  "unqualified student"?

By law your employer can only give you $5250 maximum, tax free. If your tuition was less than that, and you employer reimbursed it all; it’s  safe to assume it does not need to be reported. 

 If you got more than $5250, the amount above $5250 is usually already included in box 1 of  your w-2 and you do not need to enter anything additional on your tax return.  Since you have essentially paid tax on that part, it  is considered your after tax money and that amount can be used  to claim the tuition credit.

Q.  Is it correct to report in box 8 an unqualified student's grant income?

A. No. It is not correct for your employer to report it in box 8 of your W-2.  And it is not correct for you to put it there at the W-2 screen, in TurboTax.