Well, Obviously hay and veges are no prob, but the pellet food could be a problem.
You could try to do A non-pellet diet, but that could be highly complicated, sorry.
Although, there ARE gp foods out there without gluten in!
gd luck =)

The staples of a guinea pig’s diet are:
Timothy Hay
Pellets
Fresh Veggies

Timothy Hay is a grass hay & contains no gluten. The pellets, however, are a different story. All of them contain wheat hulls, soybean hulls, etc. So the pellets would be an issue. The fresh veggies, of course, are not an issue.

I have *heard* of people that feed their piggies a pellet-less diet, but have no firsthand experience with it. You might want to search this topic on and see what kind of info you can find. It seems that I remember it being very difficult to calculate the proper nutrient, vitamin, and caloric requirements they need each day without using pellets.

Below is a link to piggie-safe veggies that may be helpful:
Good luck!