If you ever apply for an actual professional job, you may notice that sending thank you cards is standard etiquette. At the end of of the day it's all about perception. You see it as an agreed upon formality whereas I do genuinely feel grateful. I know full well that it will not affect my chances of getting in but that makes absolutely no difference to me.
The only reason I am suggesting to ask permission is because some medical schools actively discourage thank you cards. If this was not the case, then I would always send thank you cards and encourage everyone to do the same.
However, keep in mind that I am suggesting that you ask the admissions officer if the interviewers accept thank you cards. It's no different than asking if that school accepts OOS applicants, letters of recommendation from a non-science professor or how the interviews will be structured (MMI vs panel vs traditional).