Reburying Richard III

People  seem to be missing a rather important point concerning the mortal remains of the last Plantaganet king. Richard III was laid to rest in a monastic church in Leicester. That church building was destroyed by the son of Henry VII, the Tudor usurper who had defeated Richard on Bosworth field. What is more, the Church to which Richard belonged, the Catholic Church, was similarly laid waste by the son of the first Tudor King . So how would it be right to re-inter Richard's remains in a church building confiscated by his enemy's son with a rite invented by that same pretender? There is a petition to have him reburied with Catholic rites in a Catholic Church. But in the end, I can't get too excited about all of this - leave the dead to bury their dead. We have a more pressing calling - "Come, follow me".

Which Church? Which Rite?

They think they have located Richard III's mortal remains under a Leicester car-park. So here is what is proposed: 'The Dean of Leicester, the Very Revd Vivienne Faull, said that the cathedral had worked "very closely" with Leicester City Council and the University of Leicester on the search for Richard III's remains. (she said:) "If the identity of the remains is confirmed, Leicester Cathedral will continue to work with the royal household, and with the Richard III Society, to ensure that his remains are treated with dignity and respect, and are reburied with the appropriate rites and ceremonies of the Church."'
Now the only Rites and Ceremonies known to the last Plantaganet king were those of the Holy Roman Catholic Church. So are these the rites Dean Faull envisages? And is that the Church which she expects to conduct the re-interment? I only ask, seeking as ever to be helpful.