The Bandrils' relationship with the Karfelons was sometimes friendly though occasionally there were moments of tension between the two neighboring races. The Bandrils subsisted in part on grain from Karfel. (TV: Timelash)
The Seventh Doctor recalled once fighting the Bandrils on Waterloo Bridge with "that chap from the Kinks". (AUDIO: The Quantum Possibility Engine) Ace, a former companion of the Seventh Doctor, recalled that the TARDIS was attacked by a Bandril timeship. (AUDIO: In Remembrance)
Sometime before 1969, the Bandrils were conquered by the Dominators, although that may have been part of the usual propaganda the Dominators spread on how they were in control of the Ten Galaxies. (PROSE: Mutually Assured Domination) In late October 1969, Colonel Douglas of the Fifth Operational Corps led a platoon to deal with Bandrils in the highlands of Argyll. (PROSE: The Lost Skin)
In 2018, (PROSE: Lucy Wilson and the Bledoe Cadets) the Bandrils attempted to influence the minds of children so that they would kill their parents, aiding in their takeover of the Earth. To do this they created The Billy Bandril Show, which they used to influence human minds into buying the Billy Bandril toy. Lucy Wilson and Hobo Kostinen uncovered this plan, and altered the Bandril's broadcast so that the children of Earth destroyed their Billy Bandril toys, ending the invasion. (PROSE: The Bandril Invasion)
Behind the scenes
Lance Parkin has stated that the Bandril invasion reference in The Dying Days was a joke, based on the Bandrils being "rubbish" monsters, and that "some alien invasions were beneath the Doctor's dignity to deal with".