So because it isn't actually written down anywhere in the intro, some other facts about paladins aside from the whole "religious warrior" part of it. They're actually part of the clergy and can officiate weddings or perform religious ceremonies and services--pretty much what you'd expect. The main difference between them and higher-ranking priests† is that instead of conducting services or doing much in the way of organisational or social work or theological stuff they're... meant to go out and fight. A large amount probably retire into priestly positions but in this case that's obviously not happening. They're not super common either--whilst they're common enough to see because they travel around a lot, they're like the more important priests in that there's substantially less of them in the country than knights in general (let alone men at arms if we want to get into those distinctions).
Apart from that, they get blessed equipment.
Tyaethe being Tyaethe, she just has a sword.
† You know, not the equivalent of a village or parish priest. Bishops, more or less.