We list the series based on the way they were first broadcast, not the way they were produced.

So, the question is : how where they broadcasted originally by ITV ?

Based on Rebecca answer in this previous content report, it seems that they were considered as being part of season 2.

As far as I can tell, ITV didn't specify when one season ended and another began. They aired the six episodes in question in the six weeks immediately following the airing of the final episode produced with season 2. They then took a break for the summer and aired the rest of the season 3 episodes in the fall. ITV had previously had a midseason break in airing season 1 with a 3 month gap between episodes 21 and 22.

Since the first run of the series was in syndication, ITV was only the first broadcast for about half the episodes, CBS first broadcast the other half (including the majority of season 2 and season 3). CBS released the episodes interspersed throughout season 3. Every other listing includes the episodes as part of season 3 and they have always been identified as such by The Jim Henson Company and subsequently Disney.

@mutantpanda68 said:

As far as I can tell, ITV didn't specify when one season ended and another began. They aired the six episodes in question in the six weeks immediately following the airing of the final episode produced with season 2. They then took a break for the summer and aired the rest of the season 3 episodes in the fall. ITV had previously had a midseason break in airing season 1 with a 3 month gap between episodes 21 and 22.

In this snippet from a British newspaper dated from November 2, 1978, it is clearly indicated that the new series (aka season) start on November 17, 1978. And on the November 17, 1978 TV schedule from another newspaper, it is also clearly indicated that this is a new series (aka season).