That's odd. I can't think of what else that could be. If it were rectangulare it could be one of those new outlets that directly plugs in USB devices. But a small square hole without even a notch for the phone cord clip isn't something I've ever seen. If you can't post a picture, you might want to be careful when unscrewing the plate. It might be a phone outlet, but it might not.
Sounds like it could be a plate adapted for either phone or internet, but without the connector in place. It could perhaps have been pushed out of position, or perhaps never seated properly.
The thing to do is remove the plate from the wall and see if anything's behind it. If there's a phone connection, it needs to be seated or glued into position so that the phone cord can be inserted from the other side.
One of these days we'll have a small robot that someone can move into and operate by remote control. Then we tinkerers can visit our neighbors and fix things for them.
I'm sure that's coming but first the motivated engineers over at the porn connections have to figure out the right way to create the feedback loops. Once they do that they'll become gazillionaires, but they haven't contacted me about it yet.