The Knights Templar lost the Holy Land to Saladin of Egypt in a series of battles, and were burned on crosses by the pope.

A contemporary equivalent of the Knights Templar is the Haliburton corporation.

A contemporary equivalent of the Knights of Malta, (Knights Hospitaller), is the Blackwater security agency.

Then you need to figure out what those words mean in a literary context. What is the dictionary definition of those terms? How was chivalry defined in the time period the author as writing, what were the ideals of chivalry?

Then, look at Sir Gawain’s actions throughout the story. What did he do that was chivalrous, and what did he do that wasn’t? Who did he help, and why?