I would favour keeping Croydon Tramlink on the map as it is quite a significant TfL service. It runs for quite a distance from Croydon to Wimbledon and the other lines also mainly link into rail lines. So it forms an important link between railway lines across South London. It is a lot more than a set of bus routes, sits better with rail than bus and it is largely off road.
That would be a good argument for including Croydon Tramlink in the Rail-&-Tube map: It makes sense there as a link that connects quite a few of the rail lines in South London.
But the tube map doesn't show (most) rail lines in South London, so there's no point showing something that links those unshown lines.
To my mind, the fact that it's a TfL service is irrelevant. The tube map is branded as, and is (for the most part) a
tube map, not a map of TfL services. It doesn't, for example, include TfL bus services.
The real problem with including Tramlink on the tube map is that the tube lines are really focused on central London - so the main utility of a tube map is in showing you how to get around zone 1 (and also now arguably the DLR area). If you're travelling in outer London - especially in South London, then for the most part, you need the rail & tube map - the tube map by itself is almost useless unless you happen to be travelling between destinations along the same tube line. But Tramlink doesn't go anywhere near central London - in fact, its only direct interchange with the tube at all is at Wimbledon. So it's mostly irrelevant to the kinds of journeys for which people will need the tube map. Worse - including it forces a distortion beyond belief of the South London geography on the tube map in order to fit it in. And including it but not the rail lines gives a completely misleading impression of what transport options are available in the Croydon area.
There's perhaps some case for showing the small section between Wimbledon wand Morden Road - just because of the linkage between the District and Northern lines in the area. But including the rest of it on the tube map seems to me to be a political decision that takes no account of the needs of tube map users. Croydon Tramlink should be on the rail-&-tube map, not the tube map.