This a very weird story. Apparently Archbishop Arguelles in the Phillipines read on the internet that Francis had accepted his resignation. Thing is, he never submitted one.
I've got links below to two articles covering aspects of this story. Apb. Arguelles is Tradition-friendly and offers the TLM. He had approved an apparition of Our Lady from 1948 in Lipa in which she revealed that she was the Co-Mediatrix of All Graces. The apparition had been declared unworthy of belief in the 1950's by a panel of 6 bishops, 4-2. Apparently there are news reports that two of the bishops who voted against it, including the ordinary, revealed on their deathbeds that they had been coerced into voting against it under threat of excommunication. In 2015 Apb. Aguelles reopened the case and last year found in favor of it. Francis reversed him and had all the evidence in the case, diaries, etc., destroyed and fired Apb. Arguelles. The seer reported that Our Lady had revealed some secrets to her. Were they in the diary? What was in there that caused Francis to come down so hard?
Another factor that may have come into play is that in 2014 Apb. Arguelles offered celebrets to five Franciscans of the Immaculata who had been suspended for trying to reestablish the Order after Francis suppressed it, thereby apparently enraging Francis.
There's a lot more to this story than meets the eye at first. People will have to do some searching to learn more.
Traditional Friendly Archbishop Dismissed in Filippines
The curious case of the Lipa Marian apparitions