I think the best solution would be to buy something compostable. If enough people did this, they would stop.

It always surprises me in this famously tea-drinking country how incredibly few people seem to care very much about what they are drinking as tea. You come many people who know intricate details about wine or coffee, but very rarely tea. And yet tea is so cheap, when reckoned per cup, that spending quite a bit more on good tea still works out cheaper than ordinary coffee. Unfortunately an awful lot of what is sold as quality tea, eg famous brands, is some not-very-good stuff with fancy packaging. And yet teas, like wine, vary hugely from one provenance to another, and according to when in the year they were picked. And there are good years and bad years, just like wine (2009 was a disaster in India, for example, so there is very little good tea to be had just now. Hopefully in a few months things will pick up.) If just a few people took this interest, and tea had quality labelling systems like other things from cheese to pork pies, it could be so much better.