I use seller hub so it may be slightly different on the All Selling page but it did use to be pretty much the same.
On your active listing page, tick all the items you want to edit and then click on the Edit button. That takes you to the bulk edit page. There's a dropdown menu at the top left (just above the list of items) and you click on Description, then on the next window that opens you click on Individually (I think the default is bulk). You can do them all in bulk if the wording is EXACTLY the same for that section of your description, but I think doing them in bulk only works in seller hub, not in All Selling.
When you click on individually it'll show the description of each item one and at a time and you delete what you want to, then you click on the button in the bottom of that little window that says "save and next" until they're all done. Even if you do them individually within the bulk editor it's still a lot quicker than opening each listing.
I make sure certain parts of my description are exactly the same for all my listings so that when I want to change something I can do a bulk 'find & replace', but I've found that only works properly using selling hub. If you can't delete a section in bulk you may be able to use find & replace and just put a dot in its place.
I use the HTML tab when I'm doing bulk edits so that I don't end up with extra spaces (or less).
