1. A backhandedapology, where the offending party claims regret- not for their error or discourtesy- but rather for the ill feelings or reaction for those offended. 2. What may at first appear as an apology, but after closer examination, is really a condescending or placating way to avoid personal responsibility.
HISTORY: Pope Benedict XVI deeply offended Muslims when he quoted the Byzantine emperor Manuel II Paleologus during his Regensburg talk. After an international uproar, Pope Benedict XVI attempted to apologize and clarify what he meant- along with the good intentions behind his speech- unfortunately; Pope Benedict XVI's "apology" was a bit backward.
Person 1: “I’m sorry you feel I was rude to your sister.”
Person 2: “Don’t give me a papal apology, you prick.”