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Well I guess you could just wipe the bottom of the flask (there is a large silicone pad there though which is nice per se, but not that great for wiping) - but for most people I think the problem would rather be drinking tea with sugar or cacao or whatnot out of the mug, and then putting it over the flask when done
: /Long story short: get a small (0.3 / 0.5L) one - they do not come with the mug (..but with the tea-strainer-thingy)!
I think the rocket scientist would go for the 1L version with mug -