Follow the steps in this guide to replace the home button assembly on your iPad mini 4 LTE.
Note that the iPad Mini 4 home button is paired to its original logic board, so '''replacing the original home button with a new one will disable the Touch ID function on your iPad.''' However, a replacement home button will still work as a button for click input.
Parts of this guide were shot with a Wi-Fi model and as such the internals may look slightly different from the LTE model. The procedure is the same for both models except where noted.