Cast Iron kettle seasoning

I have been using a new cast iron kettle for a couple months now and I love it! I use it at least twice a day for my green, black, oolong, and the occasional herbal teas. I get most of my tea from Adagio so I know they’re good quality, but I’ve noticed that when I get to the third or so steeping or when I’m enjoying a more delicate tea, they seem to acquire a bit of the cast iron taste. I make sure to wipe out the inside of my kettle with a damp paper towel at least every other day or every two days and I usually get a good amount of black on the towel when I wipe it down. Does it just take time to “season” the cast iron kettle similar to a skillet? Or is there some other way I should be cleaning the inside to make sure I don’t get that cast iron flavor in my teas?