There is apparently a glitch in the Turbotax software that allowed my return to claim the education credit. My parents need to file their return and claim the credit
It's not a glitch. The American Opportunity Credit can be claimed by a taxpayer who is still their parent's dependent, although the credit may be reduced. If the parents' income is too high for the credit, having the dependent claim a reduced credit is better than no credit it all.
There are two key questions. "Can you be claimed as a dependent by another taxpayer?" and "Will the taxpayer who can claim you, actually claim you this year?" If you answer yes to the first but no to the second, you will be eligible for the reduced dependent version of the AOTC. You must have answered that question incorrectly.
Your parents will claim the credit and print, sign and mail their returns. You need to file an amended return to remove the credit.