Plumbers/sink people, what is this?

I know the plastic lines with the blue connector in the foreground go to the sprayer, but this was a new one for me.

Let me back up. I'm looking for either an under sink or whole house carbon filter for the water. I knew something looked strange about the sinks plumbing, but decided to leave it alone of it worked.

Today, I decided to see what was strange about it, and how hard installing a filet would be. And that's when I found plastic lines from the 3/8 shutoff valve going directly into the faucet.

It's this delta, with a sprayer. I don't know the model, kinda hoping someone can tell me.

But it doesn't come off. I haven't tried prying under it, but nothing twists or pulls off. 

I guess aside from "what the hell is that and how am I supposed to maintain it in the future?"  My question is should I bother with an under sink with this setup at all or just get a whole house one mounted on the wall at the meter?

Looks like hot water, cold water, and a sprayer loop. 
 

But you haven't showed the end of any of them. 
 

If I'm reading it right, the faucet is held in place by the big C clip on the underside. (Plus a lot of caulk)

It definitely comes off. 

Paul nailed it. The photos are berked and stretched, but that tube that all those lines are going into should be threaded on the outside with a large nut and a c-shaped washer. That's what holds it in. Almost every time it's a pita to get a wrench on it. 

Oh. Yea I guess that rusty bit does look like A C clip.

Photos are thanks to the weird upload setup.

I need to look again then. I want regular supply lines, not integrated plastic stuff. Guess I'll look for faucets to, if they still make them with proper attachments.

In reply to RevRico :

There's all flavors out there. Lots of the hardware store stuff is plastic, but there are plenty that still use copper/brass and regular braided supply lines.