Including Martian Manhunter in Supergirl was something of a risky move, all things considered.
As many powers as the Girl of Steel has thanks to Earth’s yellow sun, Martian Manhunter could probably take her in a fair fight.
Supergirl has already had to get creative on ways to split him off from Supergirl so they aren’t too effective a team that they beat the bad guys in the first act of an episode.
Viewers may need to just get used to plot twists that give villains inexplicable methods of counteracting his telepathy.