I used to work in a tearoom, and the owner felt bad about all the spent leaves being thrown out, so she started a compost bin. Except this was just your average plastic office trash can, and it didn't get emptied into any kind of compost processing operation. Every once in a while I'd just tip the "compost" into the garbage can, until one day I saw roaches in it, at which point I emptied and cleaned the "compost bin," and hid it under some things in the cluttered basement. When she asked if I'd thrown it out, I honestly answered "no." (Maybe they pay somebody to transport it via bike to a compost operation now.)
I looked into this a little bit, and my impression was that composting is good at returning nutrients to soil for growing things or feeding worms. If you don't have a use for these things, the environmental impact is not very large. I think you have to be doing some specific things to your compost to make it perform better than a landfill in the "carbon emissions" area. If everyone cut down on their waste, yes, we'd save some gas for the garbage trucks, but "running out of landfill space" is not a present danger, and I imagine wet leaves break down pretty quickly even in a poorly-designed landfill. But hey, I could be completely wrong on all of this.
Not trying to start a big fight about this--if you compost your tea leaves, good work. If you want to start, have fun. If you don't, I just want to give you permission not to feel guilty about it, because there are plenty of more important things to do--like living in a smaller house, with a short commute preferably by bike or transit, and buying efficient appliances, for example.All that said, I did toss some tea leaves in the litter box on a few occasions.
But I imagine most methods used to dry the leaves without molding negate any environmental benefits.