Fascinating...but what would they pick out of the pockets? Practically no one had money at the time, it was one of the reasons the Templars became the traveler's cheque technology for those who were crusading and/or pilgrimageing.
The Knights Templars were the Church's "bankers". They didn't work in that capacity for regular people. They also lent money, which is a major reason why DeMolay and the other higher ups were finally murdered; the king of France didn't want to repay his loan to them!
Have you read Chaucer's famous CANTERBURY TALES? Those pilgrims carried money and all kinds of things with them!
You need to do a bit of study about life during the Middle Ages; it was somewhat different from what you assume it was.