Do you have proof it was officially part of series 3 ?

From what I could find the 2000 christmas special aired after series completed which is why it was called a special. Even if you look here https://en.wikipedia.org/wiki/List_of_The_Royle_Family_episodes which again is not firm proof being wikipedia but you can see they are listed as Special, tagged on at the end of the series. The DVD releases then bundled these specials within the series box set (see box set image art -> https://artworks.thetvdb.com/banners/seasons/75624-3.jpg).

ATM these episodes are listed twice on TMDB and whatever a moderator agrees we should go with and then merge the best metadata from both entries.