Your parents return can be rejected for many reasons. Does the reject code specifically mention a dependent?
Reject code IND-517-01 usually happens when you claim a dependent, but that person has filed a tax return and didn’t indicate that someone else can claim them as a dependent.
To fix this see How do I fix e-file reject IND-517-01?
Please look at your tax return and verify that the actual return is marked that you can be claimed. Right under your name and address, in the box with Standard Deduction, it should say, someone can claim you as a dependent with the box marked. If the box is not marked, your parents can't claim you and file electronically.
If your return is completely done processing, checks cashed and cleared, you could do an amended return and efile it. Once it is processed, your parents could file their return. Otherwise, they will need to mail it in and explain the issue. This will take months to process.