They don't know why the Invisibility Shield divine ability is behaving the way it is. But they can assume that the source of this anomaly has to be them.
After all, the capabilities of the Invisibility Shield are based on its user, not the mastery of the divine ability. So of something is wrong with this divine ability, there had to be something wrong with them.
In order to solve the mystery, they went to see their Seer and Fate Weaver. They wanted her to use her Information Identify divine ability on them to see if there is something about them that they had never noticed.
Their option was to ask a powerful Mage of the White Tower to examine them or ask a powerful Seer to have a look at them.
Mages are the most knowledgeable godclads, so a demigod mage should be able to tell what is going on with them after examining them. Legion believed this because it was the mages that discovered the advancement requirements of the various pathways and made it easier for everyone to advance.