The filter paper used to produce teabags with a string and tag attached does not need to contain plastic polymer fibres: these teabags close by folding, and are secured by stitching or stapling, rather than by heat sealing.

However, many teabag producers (including organic brands) still choose to use paper with plastic (polypropylene) fibres to add strength to their teabags.

https://treadingmyownpath.com/2018/04/05/plastic-teabags/