Have you thought about switching to loose tea?
Tea purists often say that loose leaf wins hands-down over bagged any day but did you know that tea bags often contain plastic?
If you fancy trying loose tea all you need instead of the bags a sieve, if you make pots of tea, to catch the redundant leaves as they escape the spout. If you are a one cup person, get yourself an infuser, they don't cost much. Not only will you save on plastic waste but loose tea takes up way less space than bags so much more efficient for suppliers and for your cupboards.