ineradicable

/ˌɪnɪˈrædɪkəbəl/
adjective
  1. Impossible to remove, destroy, or eliminate completely.
    • The stain on the old carpet proved ineradicable despite all cleaning efforts.
    • Some cultural traditions are so deep-rooted they seem ineradicable.
    • The memory of that day left an ineradicable mark on her heart.