"I did claim my 1098-T on my taxes not knowing the rules". Only the person who claims the student's dependency can claim the tuition credit. So, if you were not or could not be claimed as a dependent on your parent's tax return, you were probably* right to claim it, even though your parents paid the 35% that could be counted toward the credit. The $5250 of tax free tuition assistance, from your employer, should not be used in claiming the credit.
Q. Should I reimburse them (your parents) part of the 1,000.00 credited to me on my taxes?
A. That's an ethics question, not a tax question. I say yes.
*There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit. The fact that the credit was "only" $1000, would seem to indicate that you did not support yourself with earned income.
Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863
