I think remembering to take the K-cup out and letting the grounds dry helps a lot. So far this morning is the only time I tried leaving the grounds to dry.
I did not know you could get disposable liners for the my K-cup.
I have the ekobrew kind. I tap it on the side of the trash container and then rinse it, or scoop it out with a spoon and then rinse it. I don't want to wash coffee grounds down the sink so I try to get it as clean as I can before rinsing it.
My DH has a coffee maker that has a little reusable cup thing like the K cups have. He just rinses the whole thing down the sink. He doesn't tap the grounds out he just rinses them down the sink.