Keeping a Maltese coat white?

Why are you certain it's food stains? If you do think it's a food issue, change her food to something that doesn't contain beets or beet dye. That's the most common staining issue from food.

Tear stains would only effect the area around her eyes correct?

The staining is limited to her mouth (just next to and under her nose) and hind end, and her front paws recently, leading me to believe it's food stains, not tear stains. But, then again, I don't know very much about tear staining, so correct me if I'm wrong, please.

I just checked her food for any of the beet or beet dye. The only thing I could find on her soft was red dye 40, and her hard was two yellow dyes, one of which was 6, the other was 3 or 5, and blue dye 2 I believe.

So I'll be searching for a food that dosen't contain any of those dyes. I'm not going to ask her vet about it, since I have seen science diet in his waiting room, and I haven't heard very great things about it...

It's probably saliva stains, not food stains, although the dyes in the food add to the staining. Many dogs stain from saliva that don't get tear staining because the tear ducts drain properly. The stains on the faces come from the tears not draining through the duct into the sinus cavities properly.

I'd also switch her to hard food, as maltese are known to have teeth issues and the hard food would help prevent it, and wet foods almost always have dyes in them to make them more appealing to the humans buying them.