Burke continued to serve as prefect of the Apostolic Signatura until 2014. On his personal website, Burke notes that he has “written and spoken widely on Roman Catholic canon law, the Holy Eucharist, devotion to the Sacred Heart of Jesus, devotion to Our Lady of Guadalupe, and the sanctity of human life.”
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He has been publicly critical of various papal initiatives.
Burke’s public questioning of initiatives led by Pope Francis began in earnest in 2016, when he along with three other cardinals first privately submitted “dubia” — formal requests for clarification — to Pope Francis regarding the interpretation of his apostolic exhortation Amoris Laetitia, published after the 2015’s Synod on the Family. (As far as is known, the pope has never replied to those requests.) The cardinals released the dubia to the public two months later, igniting significant debate in the Church and in the media.
In an interview conducted the following year, Burke stated that he’s wrongly depicted as an “enemy” of Pope Francis but also stressed his view that current divisions in the Church demand answers to requests for clarity.
“The urgency of a response to the dubia derives from the harm done to souls by the confusion and error, which result as long as the fundamental questions raised are not answered in accord with the constant teaching and practice of the Church,” Burke said at the time.
Later on, in 2019, Burke was critical of that year’s Synod on the Pan-Amazon Region, convened by Pope Francis at the Vatican, claiming that the meeting’s working document seemed “not only in dissonance with respect to the authentic teaching of the Church, but even contrary to it.”