"We’ve worked hard to ensure that our tea bags are 99% bio degradable. However, as a result of the manufacturing process, Tetley tea bags do contain a very small amount of plastic to ensure the bags remain closed for you to enjoy your cup of tea."
Edit: The quote from the FAQ mentions the bags being biodegradable, and this page [1] about their "new biodegradable bags" shows a photo of bags without strings. So maybe it's just these stringless (and presumably cheaper to manufacture?) bags that contain plastic?
The Twinings FAQ [2] doesn't mention plastic: "Our teabags are biodegradable, plant-based teabags and will break down within 6 months if placed into a local authority compost caddy, though it may not compost as quickly if left in garden compost (as typically these are not sufficiently hot)."
[1] https://www.tetley.co.uk/sustainability/product-and-packagin...