Actually, that particular group is perfectly legitimate. It follows the traditional Tridentine Rite and has approval by the Church.
While they base themselves on the Templar tradition, they do not claim to be an extension of the Templars or anything of the sort.
The Templars were a Catholic Order that were much maligned by the King of France etc. as we know.
It is high time for the historical Catholic Templars to be rehabilitated by their Church and it is also high time for the Templar Martyrs who died in the holy Land to be given the honours of the altar e.g. 80 Templars taken captive at the Battle of Hatteen were led before a large Cross by their Saracen captors and told to spit on it. When they refused, they were beheaded. And all were beheaded.
Templars, although warriors, and based their military Rule on that written for them by St Bernard of Clairvaux.
When Jacques de Molay, the last Templar Grand Master, was about to be burned at the stake on the Seines, he asked to be tied so that he faced the Cathedral and so that his hands were tied together in the prayer position.
Other Grand Masters died in atrocious conditions in Saracen prisons for refusing to deny their Lord and Saviour.
I was to join this group, but declined as I am already a Benedictine Oblate.
Non nobis, No nobis, sed Tuo Nomine da Gloria!!
Alex