I am a provider who sends kids home with dirty socks. I have hardwood in the foyer, living area, and dining room. Tile in the kitchen and hallway. the playroom is fully carpeted and has never seen the bottom of a shoe -- EVER! I have tried for YEARS to solve the dirty sock problem and then I found the source -- the DC kids and parents!
My family takes their shoes off on the porch in spring/summer/fall or on the rug inside the foyer in bad weather. The DC parents and kids are the ones who walk into the living room, kitchen, hallways, etc with their dirty shoes. Even if it is a beautiful, dry day outside, they are carrying in tons of dirt on their shoes.
I mop as soon as I wake up each day. I run around in my own white socks all morning and they stay clean. So the floors begin the day clean. By 9am, my socks are dingy looking. The only change that has happened since I mopped is about a dozen people walking into my home with shoes on. So that is where the dirt comes from and that is why their kids socks are dirty.
I would wonder about your own habits in your providers home. Are you removing shoes before entering or immediately upon entering? Is your child? If not, you are a part of the problem and if it bothers you, you should change your habits and hope that other parents and kids follow suit.
Personally, I wouldn't ask the provider about this since you are happy otherwise. It really isn't a big deal in the grand scheme of things. As long as her home is clean otherwise, I would let it go.