What does the New York City teaching fellows answer, when you ask them that question? It's gotta be a common question for them.
That said, the simple answer is yes, you can use those payments to claim the Lifetime Learning Credit (LLC). Grad school is not eligible for the more generous American Opportunity Credit.
I don't think you'll find that exact situation covered in IRS Publication 970. But, the similar situation is "Employer Tuition assistance/reimbursement". The tax free part is not claimable but the tuition paid with the part you pay tax on (essentially your after tax money) is. The fact that your money passes thru the hands of a third party doesn't change the fact that you paid the tuition.
