Greek back in the day was written in majuscule, which would develop into what we now know as capital letters. It’s lowercase that developed later. Greek WOULDHAVELOOKEDSOMETHINGLIKETHISWITHALLCAPSANDNOSPACES.
So for one thing, the caps vs. no caps argument would be rather thin, since everything was all caps then. Whether the word should be capitalized or not in today’s translation would depend on context.
The word in question can be both Catholic and catholic, depending on whether the word is used as a part of a proper noun or as a common adjective. We refer to the Catholic Church as a proper identifier for the ecclesial communion around the see of Rome. We also refer to Catholic priests, bishops, and laity, as well as other items that pertain to this entity.
But catholic is valid as well, when it’s used to describe universality, or in contradistinction to heretical movements, as is the word “orthodox” (vs. “Orthodox”). We speak of catholic epistles, catholic belief, and in the Creed, we profess one, holy, catholic, and apostolic church. While we profess catholic, orthodox belief, we are Catholic, not Orthodox Christians.
St. Ignatius probably used the word in the “catholic” sense, that is, the Church scattered throughout the world.