How to turn off notification of comment replies?

I found the section in the site's settings to turn off the email notifications of replies to my comments, and have it set to "none", but I'm still getting them on iOS. I want to keep the stock & article mobile notifications, so I don't want to turn off notifications for the app entirely, but I don't want a popup notification on my phone anytime someone in the comment section feels like they just have to get the last word in. I can check that on the website, I really don't want the additional distraction for something that's nowhere near as important as stock news notifications. 

Has anyone figured out how to turn off just the comment reply notifications on mobile?