First off welcome to the forum. It is good to have you here.

If this is a deep rusting process, it would be apparent that it did not form in two days. This should rifle should be taken back to the dealer and you should ask for a new rifle. Anyone would be able to understand that the rust is "old" and therefore not your fault. If the dealer will not do anything about it, contact Thompson Center and see what kind of satisfaction they can offer.

If this is just a light surface rust, some solvent and a strong cleaning will often times remove it. Then make sure you use a high quality gun oil and protect those surfaces. I personally like a brass tooth brush to use, when I scrub that area.

Good luck with your rifle. It sounds like the rifle is a lot more intricate then I initially thought them to be. The simplicity they suggest in their commercials might be a little short stressed if these are areas of concern as well.