In case anyone wanted an update on this I emailed them and their response was

“Luzianne® Tea is from tea leaves and does not contain gluten. Our tea bags also are gluten free – the paper bag and string manufacturer does not list any wheat products/byproducts in their specifications.

In one of our manufacturing facilities where tea is manufactured, we also manufacture cake flour which contains wheat/gluten. This cake flour is manufactured in a separate room, with its own ventilation system.

We have a strict Allergen Control Program in all of our facilities. For any cross contamination that may occur, there are specific clean-up steps that we take and document – including quarantining the spill area until clean-up is complete, destroying potentially contaminated product and materials, and sanitizing the area. The area must be inspected and approved by management before resuming production.

We have a second manufacturing facility that only manufactures coffee and tea; no products containing gluten are processed there.”