Not to concern you, and not sure if this is still valid information as I'm speaking to smart phone screens in general and not necessarily Apple related, but all screens come with an oleophobic coating out of the box. This coating is designed to resist the oils on your fingers, in order to limit finger printing.
A benefit of this coating is that, when the phone is new and the coating is uniform and pristine, your finger will glide effortlessly across the screen with very little friction. As time goes on you will notice more fingerprinting and more friction, as the coating wears away. Usually around a years time, you'll have very little coating and a pretty sticky screen. It's not a big deal usually, to me anyway, because by then I've beat the crap out of my phone anyway and have gotten countless amounts of crap on it, so I don't really notice or find it unreasonable that the phone isn't pristine.
One of the downsides of using a screen protector is that they can damage/ruin this coating. And it's possible you did that already, as I've done that to mine in the past. That being said, if you're going to use a protector anyway, does it really matter? You aren't going to be touching the actual screen, so who cares if you damage the coating? The protectors come with this coating applied, so they feel the same as phones screens. These coatings too, wear away, but with a protector you can just apply another one and be on your way.
One more note, you can get oleophobic coating kits, if you really want to reapply a coating to a phone, but I don't think they are recommended as they are pretty tough to use and perfect.
Chances are you didn't damage your coating, you're probably fine. Even if you did damage it, probably only to the point where it would have been damaged in a weeks worth of use anyway. The coatings really don't last very long, as I'm sure you've noticed on your phone screen when you see an enormous amount of fingerprinting/oil.