I'm glad you took pictures!

In defense (just a tiny bit) of the guys, putting loose rugs down on carpet could be a very difficult way to move a two-wheeler cart (heavy with an appliance) across a room. There is special plastic for this, and you can tape it down to your carpet with special tape. I've seen this done at open houses, for example.

But still -- they couldn't wipe their shoes off at the door? Warn you that it was muddy or something?

However, my defense of Lowe's ends right there. If you don't hear back from Lowes SOON, you need to send them a formal demand letter with a specific date (such as, 10 or 14 days after the date you send the letter) by which you expect to hear from them. Send it to the manager of the store and cc in-house counsel (which should be easy to find via their website, or by calling their HQ). Send it by certified mail, return receipt request, or by a delivery service such as FedEx, which will require them to sign for it, and you can get that proof.

Then take them to small claims court.

You must be furious, although you've written a pretty even-toned letter.

GOOD LUCK!