The process for selection of a Grand Master of the Order is specified in its Constitutional Charter and the Order's Code.  The supreme head of the Order is the Grand Master, who is elected for life by the Council Complete of State and is in no way subject to the Holy Father nor does he derive his authority in any way from the Holy See.

Therefore the Holy Father cannot remove Matthew Festing.

The Patron's position relative to the Knights is roughly equivalent to a secular ambassador to a country. He promotes the spiritual interests of the Order and its relations with the Holy See.

The Holy Father can remove the Patron at will. However, the Patron cannot interfere in the internal governance of the Order.