Are you hearing it when it says "dre"? It may be the combination of the d sound coupled with the back-of-the-throat r; that's the only part that sounds kind of like a 'p'.
I think it might be a mix of an odd sound combination and the program generating the speech. I've noticed it's has some trouble with the r's occasionally, typically erring on the side of making them too quiet or soft, which in this case is mimicking a "p" sound. I don't know if it is something really fixable :( I think we might just have to practice getting an ear for the throaty r.
Well normally there isn't a /p/ in forældre, since its pronunciation in IPA is [fʌˈεlˀdʁʌ].
I understood De er ikke mine...forældre, but the pronuntiation of " rigtige" sounded like a different word. My ears apologize...!
A more accurate English translation would be "they are not my actual (in the sense of right) parents" . No English speaker would ever say they are not my real parents. It is much too awkward, insensitive and crude.