Percy
It was bound to happen eventually. After all, Percy is one of the most powerful demigods of all time. Add in a daughter of Athena to the mix and you have a recipe for disaster. So it was no surprise when a gorgon came and attacked you guys while Percy was at work. Once Percy got home and saw the monster dust and a scary-looking Annabeth holding a crying you close to her chest, he really didn't need an explanation. Instead of asking for one, he just hugged the both of you close to him nearly crying himself, realizing he could have easily lost you if Annabeth wasn't there.
Jason
You guys live in New Rome. No monster attacks for you!
Leo
Magical tech monster shield. It's Leo.
Nico
Most of the monster population, about 99.99% of it, live in the United States due to it being the Flame of the West. And it's because that's where all the demigods are so.... Basically, Nico literally has zero problems with monsters. (You guys are in Italy) The only things for him to actually worry about is getting caught by the government and keeping you happy, healthy and safe.
Edit 6/14/18: Just doing some maintenance
