Taggy-lens allows us to use lenses to parse and inspect HTML documents.
#!/usr/bin/env stack
-- stack --resolver lts-7.0 --install-ghc runghc --package text --package lens --package taggy-lens
{-# LANGUAGE OverloadedStrings #-}
import qualified Data.Text.Lazy as TL
import qualified Data.Text.IO as T
import Text.Taggy.Lens
import Control.Lens
someHtml :: TL.Text
someHtml =
    "\
    \<!doctype html><html><body>\
    \<div>first div</div>\
    \<div id=\"thediv\">second div</div>\
    \<div id=\"not-thediv\">third div</div>"
main :: IO ()
main = do
    T.putStrLn
        (someHtml ^. html . allAttributed (ix "id" . only "thediv") . contents)
Find div with id="article" and strip out all the inner script tags.
#!/usr/bin/env stack
-- stack --resolver lts-7.1 --install-ghc runghc --package text --package lens --package taggy-lens --package string-class --package classy-prelude
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE OverloadedStrings #-}
import ClassyPrelude
import Control.Lens hiding (children, element)
import Data.String.Class (toText, fromText, toString)
import Data.Text (Text)
import Text.Taggy.Lens
import qualified Text.Taggy.Lens as Taggy
import qualified Text.Taggy.Renderer as Renderer
somehtmlSmall :: Text
somehtmlSmall =
    "<!doctype html><html><body>\
    \<div id=\"article\"><div>first</div><div>second</div><script>this should be removed</script><div>third</div></div>\
    \</body></html>"
renderWithoutScriptTag :: Text
renderWithoutScriptTag =
    let mArticle :: Maybe Taggy.Element
        mArticle =
            (fromText somehtmlSmall) ^? html .
            allAttributed (ix "id" . only "article")
        mArticleFiltered =
            fmap
                (transform
                     (children %~
                      filter (\n -> n ^? element . name /= Just "script")))
                mArticle
    in maybe "" (toText . Renderer.render) mArticleFiltered
main :: IO ()
main = print renderWithoutScriptTag
-- outputs:
-- "<div id=\"article\"><div>first</div><div>second</div><div>third</div></div>"
Contribution based upon @duplode's SO answer