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Re:Two Decades of Recommender Systems at Amazon.com by Deimorz on Wednesday July 05, 2017 @08:36PM (#14707333)
You can go into your viewing activity (only available from your account page on the desktop site, I think) and delete the show from there, and then it should remove it from "Continue Watching".

It's not an obvious or straightforward thing to need to do, but seems to work.

Re:Two Decades of Recommender Systems at Amazon.com by NoCoastCoder on Wednesday July 05, 2017 @09:26PM (#14707524)
That's definitely available in the app as well.