It looks like that is a recessed aerator or maybe a tamper proof aerator. Unsure if those are the same thing, but they were common terms when I was searching for that issue. If you're not able to twist it off that might be the case. My bathroom has something similar. When I did a quick search it looked like there was a special tool or key to remove it, however, I saw some people were successful with using the prongs on a fork, needle nose pliers, or even a flat blade screw driver. Never tried it though.
It looks like Delta has a slew of faucets with that design. Perhaps yours is one of them?