A family of Microsoft word processing software products for creating web, email, and print documents.
I think you're referring to a bookmark around text inside a document. You're correct that the Bookmark button's menu on the Insert ribbon in Word Online doesn't contain a Delete item (although it would be nice if it did). The procedure is quite different from the one in desktop Word.
Start by clicking the bookmark symbol in the left margin near the bookmarked text. That will highlight the text and show square brackets around it. Now right-click the text, and you'll find a Remove Bookmark item in the menu.