Osbourne, 29, whose sister Kelly quit the E! fashion series at the end of February, hinted that there was a hypocrisy surrounding both recent exits, reported Digital Spy.
"So Kelly quits and she's overreacting, Kathy quits and she's a hero? I find this frustrating," Jack wrote on Facebook.
Griffin announced her exit from "Fashion Police" after just seven episodes on the show.
The comedian said that she discovered her "style does not fit" with the show.
Kelly had previously left the series to pursue other opportunities, just days after threatening the leave over a joke made by co-host Giuliana Rancic about actress Zendaya.
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