No, the leadership of the Knights does not take religious vows and are therefore not personally under obedience to the Holy See.

Since 1630 the supreme head of the Order, the Grand Master, holds the "precedence" of a cardinal of the Church, but this is an honorific and of no significance.

The Pope appoints the prelate of the order to supervise the clergy associate with the order from among three candidates proposed by the Grand Master. His jurisdiction extends only to the clergy, not the organization or the religious in it.

The Pope is unlikely to withdraw anyone since the Knights support the clergy, the religious (including two cloistered convents dating back hundreds of years, and their missions in providing for the poor and others the Knights assist.